SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Size: px
Start display at page:

Download "SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question."

Transcription

1 Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees. Find the expected frequencies for each class to determine if the employee ages are normally distributed. Class boundaries Frequency, f Perform a Chi-square Goodness-of-fit-test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic χ2 to test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. Starting Position Number of Wins A) B) C) D) ) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Find the critical value χ 2 0 to test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. Starting Position Number of Wins A) B) C) D) Page 209

2 3) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. Starting Position Number of Wins MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic χ2 to test the claim that the distribution is uniform.. Brand Customers A) B) C) D) ) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Find the critical value χ 2 0 to test the claim that the distribution is uniform. Use α = Brand Customers A) B) C) D) ) A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the distribution is uniform. Use α = Brand Customers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic χ2 to determine if the grade distribution for the department is different than expected. Grade A B C D F Number A) 5.25 B) 6.87 C) 3.41 D) 4.82 Page 210

3 8) A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Find the critical value χ 2 0 to determine if the grade distribution for the department is different than expected. Use α = Grade A B C D F Number A) B) C) D) ) A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Determine if the grade distribution for the department is different than expected. Use α = Grade A B C D F Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) Each side of a standard six-sided die should appear approximately 1 6 of the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below. Calculate the chi-square test statistic χ2 to test the playerʹs claim. Number Frequency A) B) C) D) ) Each side of a standard six-sided die should appear approximately 1 6 of the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below. Find the critical value χ 2 0 to test the playerʹs claim. Use α = Number Frequency A) B) C) D) ) Each side of a standard six-sided die should appear approximately 1 6 of the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below. Test the playerʹs claim. Use α = Number Frequency Page 211

4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 13) A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the group, 31% for the group, and 12% for the group over 65. Calculate the chi-square test statistic χ2 to test the claim that all ages have crash rates proportional to their driving rates. Age Under Over 65 Drivers A) B) C) D) ) A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the group, 31% for the group, and 12% for the group over 65. Find the critical value χ 2 0 to test the claim that all ages have crash rates proportional to their driving rates. Use α = Age Under Over 65 Drivers A) B) C) D) ) A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the group, 31% for the group, and 12% for the group over 65. Test the claim that all ages have crash rates proportional to their driving rates. Use α = Age Under Over 65 Drivers ) A sociologist believes that the levels of educational attainment of homeless persons are not uniformly distributed. To test this claim, you randomly survey 100 homeless persons and record the educational attainment of each. The results are shown in the following table. Calculate the chi-square test statistic χ2 to test the sociologistʹs claim. Response Frequency, f Less than high school 38 High school graduate/g.e.d. 34 More than high school 28 Page 212

5 17) A sociologist believes that the levels of educational attainment of homeless persons are not uniformly distributed. To test this claim, you randomly survey 100 homeless persons and record the educational attainment of each. The results are shown in the following table. Find the critical value χ0 2 to test the sociologistʹs claim. Use α = Response Frequency, f Less than high school 38 High school graduate/g.e.d. 34 More than high school 28 18) A sociologist believes that the levels of educational attainment of homeless persons are not uniformly distributed. To test this claim, you randomly survey 100 homeless persons and record the educational attainment of each. The results are shown in the following table. At α = 0.10, is there evidence to support the sociologistʹs claim that the distribution is not uniform? Response Frequency, f Less than high school 38 High school graduate/g.e.d. 34 More than high school 28 3 Test for Normality Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees. Are the ages of employees normally distributed? Use α = Class boundaries Frequency, f Page 213

6 10.2 Independence 1 Find Expected Frequencies MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The contingency table below shows the results of a random sample of 400 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Party Republican Democrat Independent Opinion Approve Disapprove No Opinion Find the expected frequency for the cell E2,2. Round to the nearest tenth if necessary. A) 55.2 B) 45.6 C) D) ) A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Round to the nearest tenth if necessary. Gender Male Female Minutes spent online per day over A) 33 B) 49.3 C) 44 D) ) A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Find the expected frequency E2,2 to test the claim that walking and low, moderate, and high blood pressure are not related. Round to the nearest tenth if necessary. Blood Pressure Low Moderate High Walkers Non-walkers A) 61.8 B) 29.5 C) 66.2 D) ) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Find the expected frequency for E2,2 to test the claim that the number of home team and visiting team wins are independent of the sport. Round to the nearest tenth if necessary. Football Basketball Soccer Baseball Home team wins Visiting team wins A) B) 18.2 C) D) 24.8 Page 214

7 2 Perform a Chi-square Test for Independence MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Use α = Party Republican Democrat Independent Opinion Approve Disapprove No Opinion Find the critical value χ 2 0, to test the claim of independence. A) B) C) D) ) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Party Republican Democrat Independent Opinion Approve Disapprove No Opinion Find the chi-square test statistic, χ2, to test the claim of independence. A) B) C) D) ) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Party Republican Democrat Independent Opinion Approve Disapprove No Opinion Test the claim of independence. Page 215

8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the critical value χ 2 0 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Use α = Gender Male Female Minutes spent online per day over A) B) C) D) ) A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square statistic χ2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Gender Male Female Minutes spent online per day over A) B) C) D) ) A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Is there enough evidence to conclude that the number of minutes spent online per day is related to gender? Use α = Gender Male Female Minutes spent online per day over MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Find the critical value χ 2 0 to test the claim that walking and low, moderate, and high blood pressure are not related. Use α = Blood Pressure Low Moderate High Walkers Non-walkers A) B) C) D) Page 216

9 8) A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Calculate the chi-square test statistic χ2 to test the claim that walking and low, moderate, and high blood pressure are not related. Blood Pressure Low Moderate High Walkers Non-walkers A) B) C) D) ) A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Test the claim that walking and low, moderate, and high blood pressure are not related. Use α = Blood Pressure Low Moderate High Walkers Non-walkers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Find the critical value χ 2 0 to test the claim that the number of home team and visiting team wins is independent of the sport. Use α = Football Basketball Soccer Baseball Home team wins Visiting team wins A) B) C) D) ) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Calculate the chi-square test statistic χ2 to test the claim that the number of home team and visiting team wins is independent of the sport. Football Basketball Soccer Baseball Home team wins Visiting team wins A) B) C) D) Page 217

10 12) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Test the claim that the number of home team and visiting team wins is independent of the sport. Use α = Football Basketball Soccer Baseball Home team wins Visiting team wins ) The data below shows the age and favorite type of music of 779 randomly selected people. Test the claim that age and preferred music type are independent. Use α = Age Country Rock Pop Classical Perform a Homogeneity of Proportions Test Provide an appropriate response. 1) A random sample of 400 men and 400 women was randomly selected and asked whether they planned to vote in the next election. The results are listed below. Perform a homogeneity of proportions test to test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote. Use α = Men Women Plan to vote Do not plan to vote ) A random sample of 100 students from 5 different colleges was randomly selected, and the number who smoke was recorded. The results are listed below. Perform a homogeneity of proportions test to test the claim that the proportion of students who smoke is the same in all 5 colleges. Use α = Colleges Smoker Nonsmoker Page 218

11 10.3 Comparing Two Variances 1 Find the Critical F-value for a Right-tailed Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the critical value F0 for a two-tailed test using α = 0.05, d.f.n = 5, and d.f.d = 10. A) 4.24 B) 4.07 C) 4.47 D) ) Find the critical value F0 for a one-tailed test using α = 0.01, d.f.n = 3, and d.f.d = 20. A) 4.94 B) C) 5.82 D) ) Find the critical value F0 for a one-tailed test using α = 0.05, d.f.n = 6, and d.f.d = 16. A) 2.74 B) 3.94 C) 2.66 D) ) Find the critical value F0 for a two-tailed test using α = 0.02, d.f.n = 5, and d.f.d = 10. A) 5.64 B) C) 5.99 D) ) Find the critical value F0 to test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 25 n2 = 30 s 2 1 = 3.61 s 2 2 = 2.25 A) 2.15 B) 2.21 C) 2.14 D) ) Find the critical value F0 to test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 13 n2 = 12 s 2 1 = 7.84 s 2 2 = 6.25 A) 4.40 B) 2.79 C) 4.25 D) 3.43 Page 219

12 7) Find the critical value F0 to test the claim that σ 2 1 > σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 16 n2 = 13 s 2 1 = 1600 s 2 2 = 625 A) 4.01 B) 3.18 C) 2.62 D) ) Find the critical value F0 to test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 16 n2 = 15 s 2 1 = 8.41 s 2 2 = 7.84 A) 2.46 B) 3.66 C) 2.95 D) ) Find the critical value F0 to test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 11 n2 = 18 s 2 1 = s 2 2 = A) 3.59 B) 2.45 C) 2.92 D) Test a Claim About the Differences Between Two Population Variances MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Calculate the test statistic F to test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 25 n2 = 30 s 2 1 = s 2 2 = A) B) C) D) Page 220

13 2) Calculate the test statistic F to test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 13 n2 = 12 s 2 1 = s 2 2 = A) B) C) D) ) Calculate the test statistic F to test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 13 n2 = 12 s 2 1 = s 2 2 = A) B) C) D) ) Calculate the test statistic F to test the claim that σ 2 1 > σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 16 n2 = 13 s 2 1 = 12,800 s 2 2 = 5000 A) B) C) D) ) Calculate the test statistic F to test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 16 n2 = 15 s 2 1 = s 2 2 = A) B) C) D) Page 221

14 6) Calculate the test statistic F to test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. n1 = 11 n2 = 18 s 2 1 = 1.156> s 2 2 = 0.52 A) B) C) D) ) Test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 25 n2 = 30 s 2 1 = s 2 2 = ) Test the claim that σ 2 1 = σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 13 n2 = 12 s 2 1 = s 2 2 = ) Test the claim that σ 2 1 > σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 16 n2 = 13 s 2 1 = 3200 s 2 2 = ) Test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 16 n2 = 15 s 2 1 = s 2 2 = Page 222

15 11) Test the claim that σ 2 1 σ 2 2. Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α = n1 = 11 n2 = 18 s 2 1 = s 2 2 = ) A local bank claims that the variance of waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting time at both banks. The sample statistics are listed below.test the local bankʹs claim. Use α = Local Bank Competitor Bank n1 = 13 n2 = 16 s1 = 0.66 minutes s2 = 0.78 minutes 13) A study was conducted to determine if the variances of elementary school teacher salaries from two neighboring districts were equal. A sample of 25 teachers from each district was selected. The first district had a standard deviation of s1 = $3680, and the second district had a standard deviation s2 = $3360. Test the claim that the variances of the salaries from both districts are equal. Use α = ) A random sample of 21 women had blood pressure levels with a variance of A random sample of 18 men had blood pressure levels with a variance of Test the claim that the blood pressure levels for women have a larger variance than those for men. Use α = ) The weights of a random sample of 121 women between the ages of 25 and 34 had a standard deviation of 28 pounds. The weights of 121 women between the ages of 55 and 64 had a standard deviation 21 pounds. Test the claim that the older women are from a population with a standard deviation less than that for women in the 25 to 34 age group. Use α = ) At a college, 61 female students were randomly selected and it was found that their monthly income had a standard deviation of $ For 121 male students, the standard deviation was $ Test the claim that variance of monthly incomes is higher for male students than it is for female students. Use α = ) A medical researcher suspects that the variance of the pulse rate of smokers is higher than the variance of the pulse rate of non-smokers. Use the sample statistics below to test the researcherʹs suspicion. Use α = Smokers Non-smokers n1 = 61 n2 = 121 s1 = 9.36 s2 = 6.36 Page 223

16 18) A statistics teacher believes that the variances of test scores of students in her evening statistics class are lower than the variances of test scores of students in her day class. The results of an exam, given to the day and evening students, are shown below. Can the teacher conclude that her evening students have a lower variance? Use α = Day Students Evening Students n1 = 31 n2 = 41 s1 = 34.3 s2 = ) A statistics teacher wants to see whether there is a significant difference in the variances of the ages between day students and night students. A random sample of 31 students is selected from each group. The data are given below. Test the claim that there is no difference in age between the two groups. Use α = Day Students Evening Students ) A local bank claims that the variance of waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting time at both banks. The sample statistics are listed below.test the local bankʹs claim. Use α = Local Bank Competitor Bank n1 = 41 n2 = 61 s1 = 1.65 minutes s2 = 3 minutes 3 Find the Critical F-value for a Left-tailed Test Provide an appropriate response. 1) Find the left-tailed and right tailed critical F-values for a two-tailed test. Let α = 0.02, d.f.n = 7, and d.f.d = 5. 2) Find the left-tailed and right tailed critical F-values for a two-tailed test. Use the sample statistics below. Let α = n1 = 5 n2 = 6 s 2 1 = 5.8 s 2 2 = 2.7 Page 224

17 4 Construct the Indicated Confidence Interval Provide an appropriate response. 1) The weights of a random sample of 25 women between the ages of 25 and 34 had a standard deviation of 28 pounds. The weights of a random sample of 41 women between the ages of 55 and 64 had a standard deviation of 21 pounds. Construct a 95% confidence interval for σ 1 2 σ2 2, where σ 1 2 and σ2 2 are the variances of the weights of women between the ages 25 and 34 and the weights of women between the ages of 55 and Analysis of Variance 1 Perform a One-way ANOVA Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the critical F0-value to test the claim that the populations have the same mean. Use α = Brand 1 Brand 2 Brand 3 n = 8 n = 8 n = 8 x = 3.0 x = 2.6 x = 2.6 s = 0.50 s = 0.60 s = 0.55 A) 3.47 B) C) D) ) Find the test statistic F to test the claim that the populations have the same mean. Brand 1 Brand 2 Brand 3 n = 8 n = 8 n = 8 x = 3.0 x = 2.6 x = 2.6 s = 0.50 s = 0.60 s = 0.55 A) B) C) D) ) Test the claim that the populations have the same mean. Use α= Brand 1 Brand 2 Brand 3 n = 8 n = 8 n = 8 x = 3.0 x = 2.6 x = 2.6 s = 0.50 s = 0.60 s = 0.55 Page 225

18 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjectʹs blood pressure is recorded. Find the critical value F0 to test the claim that there is no difference among the means. Use α = Group 1 Group 2 Group A) 3.68 B) C) 4.77 D) ) A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjectʹs blood pressure is recorded. Find the test statistic F to test the claim that there is no difference among the means. Group 1 Group 2 Group A) B) C) D) ) A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjectʹs blood pressure is recorded. Test the claim that there is no difference among the means. Use α = Group 1 Group 2 Group Page 226

19 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Find the critical value F0 to test the claim that the type of fertilizer makes no difference in the mean number of raspberries per plant. Use α = Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer A) 4.94 B) 4.43 C) D) ) Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Find the test statistic F to test the claim that the type of fertilizer makes no difference in the mean number of raspberries per plant. Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer A) B) C) D) ) Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Test the claim that the type of fertilizer makes no difference in the mean number of raspberries per plant. Use α = Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer Page 227

20 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find the critical value F0 to test the claim that there is no difference in the average age of each group. Use α = Elementary Teachers High School Teachers Community College Teachers A) 6.36 B) 5.09 C) 9.43 D) ) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find the test statistic F to test the claim that there is no difference in the average age of each group. Elementary Teachers High School Teachers Community College Teachers A) B) C) D) ) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Test the claim that there is no difference in the average age of each group. Use α = Elementary Teachers High School Teachers Community College Teachers Page 228

21 13) The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Test the claim that there is no difference in the mean grade point averages of the 3 groups. Use α = Tennis Golf Swimming ) The times (in minutes) to assemble a computer component for 3 different machines are listed below. Workers are randomly selected. Test the claim that there is no difference in the mean time for each machine. Use α = Machine 1 Machine 2 Machine ) A realtor wishes to compare the square footage of houses in 4 different cities, all of which are priced approximately the same. The data are listed below. Can the realtor conclude that the mean square footage in the four cities are equal? Use α = City #1 City #2 City #3 City # Page 229

22 16) A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood-pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjectʹs blood pressure is recorded. Perform a Scheffé Test to determine which means have a significance difference. Use α = Group 1 Group 2 Group ) Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Perform a Scheffé Test to determine which means have a significance difference. Use α = Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer Page 230

23 Ch. 10 Chi SquareTests and the F-Distribution Answer Key 10.1 Goodness of Fit 1 Find Expected Frequencies 1) 11, 26, 32, 21, and 7, respectively. 2 Perform a Chi-square Goodness-of-fit-test 1) A 2) A 3) critical value χ 2 0 = ; chi-square test statistic χ ; fail to reject H0; There is not sufficient evidence to reject the claim that the distribution is uniform. 4) A 5) A 6) critical value χ 2 0 = ; chi-square test statistic χ ; reject H0; There is sufficient evidence to reject the claim that the distribution is uniform. 7) A 8) A 9) critical value χ 2 0 = ; chi-square test statistic χ ; fail to reject H0; There is not sufficient evidence to support the claim that the grades are different than expected. 10) A 11) A 12) critical value χ 2 0 = 9.236; chi-square test statistic χ ; fail to reject H0; There is not sufficient evidence to support the claim of a loaded die. 13) A 14) A 15) critical value χ 2 0 = 7.815; chi-square test statistic χ ; reject H0; There is sufficient evidence to reject the claim that all ages have the same crash rate. 16) ) ) Critical value χ0 2 = 4.605; chi-square test statistic χ2 = 1.520; fail to reject H0; There is not enough evidence to support the claim that the distribution is not uniform. 3 Test for Normality 1) Critical value χ0 2 = 9.488; chi-square test statistic χ2 = 1.77; fail to reject H0; The ages of employees are normally distributed Independence 1 Find Expected Frequencies 1) A 2) A 3) A 4) A 2 Perform a Chi-square Test for Independence 1) A 2) A Page 231

24 3) critical value χ 2 0 = 9.488; chi-square test statistic χ ; fail to reject H0; There is not enough evidence to conclude that the representativeʹs opinion on a bill is related to their party affiliation. 4) A 5) A 6) critical value χ 2 0 = 7.815; chi-square test statistic χ ; reject H0; There is enough evidence to conclude that the number of minutes spent online per day is related to gender. 7) A 8) A 9) critical value χ 2 0 = 9.210; chi-square test statistic χ ; fail to reject H0; There is enough evidence to conclude that walking is not related to low, moderate, or high blood pressure. 10) A 11) A 12) critical value χ 2 0 = ; chi-square test statistic χ ; fail to reject H0; There is enough evidence to conclude that home team wins and visiting team wins are independent of the sport. 13) critical value χ 2 0 = ; chi-square test statistic χ ; reject H0; There is sufficient evidence to reject the claim of independence. 3 Perform a Homogeneity of Proportions Test 1) critical value χ 2 0 = 3.841; chi-square test statistic χ ; fail to reject H0; There is not sufficient evidence to reject the claim. 2) critical value χ 2 0 = ; chi-square test statistic χ ; reject H0; There is sufficient evidence to reject the claim Comparing Two Variances 1 Find the Critical F-value for a Right-tailed Test 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 2 Test a Claim About the Differences Between Two Population Variances 1) A 2) A 3) A 4) A 5) A 6) A 7) critical value F0 = 2.15; test statistic F 1.604; fail to reject H0; There is not sufficient evidence to reject the claim. 8) critical value F0 = 4.40; test statistic F 1.254; fail to reject H0; There is not sufficient evidence to reject the claim. 9) critical value F0 = 4.01; test statistic F 2.560; fail to reject H0; There is not sufficient evidence to support the claim. Page 232

25 10) critical value F0 = 2.46; test statistic F 1.073; fail to reject H0; There is not sufficient evidence to reject the claim. 11) critical value F0 = 3.59; test statistic F 2.223; fail to reject H0; There is not sufficient evidence to support the claim. 12) critical value F0 = 2.48; test statistic F 1.397; fail to reject H0; There is not sufficient evidence to reject the claim. 13) critical value F0 = 2.27; test statistic F 1.200; fail to reject H0; There is not sufficient evidence to reject the claim. 14) critical value F0 = 3.16; test statistic F 1.502; fail to reject H0; There is not sufficient evidence to support the claim. 15) critical value F0 = 1.35; test statistic F 1.778; reject H0; There is sufficient evidence to support the claim. 16) critical value F0 = 1.73; test statistic F 1.928; reject H0; There is sufficient evidence to support the claim. 17) critical value F0 =1.43; test statistic F 2.166; reject H0; There is sufficient evidence to support the claim. 18) critical value F0 =2.20; test statistic F 3.419; reject H0; There is sufficient evidence to support the claim. 19) critical value F0 = 2.07; test statistic F 1.549; fail to reject H0; There is not sufficient evidence to reject the claim. 20) critical value F0 = 1.64; test statistic F 3.306; reject H0; There is sufficient evidence to support the claim. 3 Find the Critical F-value for a Left-tailed Test 1) FL = 0.134, FR = ) FL = 0.107, FR = Construct the Indicated Confidence Interval 1) < σ 1 2 σ2 2 < Analysis of Variance 1 Perform a One-way ANOVA Test 1) A 2) A 3) critical value F0 = 3.47; test statistic F 1.403; fail to reject H0; The data does not provide enough evidence to indicate that the means are unequal. 4) A 5) A 6) critical value F0 = 3.68; test statistic F ; reject H0; There is enough evidence that the sample means are 7) A 8) A 9) critical value F0 = 4.94; test statistic F 8.357; reject H0; The data provides ample evidence that the sample means are unequal. 10) A 11) A 12) critical value F0 = 6.36; test statistic F 2.517; fail to reject H0; There is not enough evidence to indicate that the means are different. 13) critical valuef0 = 3.89; test statistic F 1.560; fail to reject H0; The data does not provide enough evidence to indicate that the means are unequal. 14) critical value F0 = 6.51; test statistic F 7.103; reject H0; There is enough evidence that the sample means are different. 15) critical value F0 = 5.09; test statistic F ; reject H0; There is enough evidence that the sample means are 16) critical value F0 = 7.36; Test statistic F 22.0 for Group #1 versus Group #2 indicating a significant difference. Test statistic F 6.5 for Group #1 versus Group #3 indicating no difference. Test statistic F 4.6 for Group #2 versus Group #3 indicating no difference. 17) critical value F0 = 14.82; Test statistic F for #1 vs #2 indicating no difference. Test statistic F for #1 vs #3 indicating a significant difference. Test statistic F for #1 vs #4 indicating no difference. Test statistic F for #2 vs #3 indicating no difference. Test statistic F 7.04 for #2 vs #4 indicating no difference. Test statistic F for #3 vs #4 indicating no difference. Page 233

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

More information

Chapter Additional: Standard Deviation and Chi- Square

Chapter Additional: Standard Deviation and Chi- Square Chapter Additional: Standard Deviation and Chi- Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret

More information

Null Hypothesis H 0. The null hypothesis (denoted by H 0

Null Hypothesis H 0. The null hypothesis (denoted by H 0 Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property

More information

CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

More information

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

More information

Mind on Statistics. Chapter 8

Mind on Statistics. Chapter 8 Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

More information

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING MULTIPLE CHOICE 56. In testing the hypotheses H 0 : µ = 50 vs. H 1 : µ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized

More information

Mind on Statistics. Chapter 15

Mind on Statistics. Chapter 15 Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,

More information

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700 Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,

More information

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing

More information

Review #2. Statistics

Review #2. Statistics Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of

More information

C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters. Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

More information

Section 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)

Section 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935) Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis

More information

Mind on Statistics. Chapter 10

Mind on Statistics. Chapter 10 Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine

More information

Stats Review Chapters 9-10

Stats Review Chapters 9-10 Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice! Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice

More information

Math 108 Exam 3 Solutions Spring 00

Math 108 Exam 3 Solutions Spring 00 Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8

More information

The Chi-Square Test. STAT E-50 Introduction to Statistics

The Chi-Square Test. STAT E-50 Introduction to Statistics STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0. Ch. 5 Normal Probability Distributions 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 1 Find Areas Under the Standard Normal Curve 1) Find the area under the standard normal

More information

Chapter 7 TEST OF HYPOTHESIS

Chapter 7 TEST OF HYPOTHESIS Chapter 7 TEST OF HYPOTHESIS In a certain perspective, we can view hypothesis testing just like a jury in a court trial. In a jury trial, the null hypothesis is similar to the jury making a decision of

More information

1) The table lists the smoking habits of a group of college students. Answer: 0.218

1) The table lists the smoking habits of a group of college students. Answer: 0.218 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

Sample Term Test 2A. 1. A variable X has a distribution which is described by the density curve shown below:

Sample Term Test 2A. 1. A variable X has a distribution which is described by the density curve shown below: Sample Term Test 2A 1. A variable X has a distribution which is described by the density curve shown below: What proportion of values of X fall between 1 and 6? (A) 0.550 (B) 0.575 (C) 0.600 (D) 0.625

More information

Introduction to Analysis of Variance (ANOVA) Limitations of the t-test

Introduction to Analysis of Variance (ANOVA) Limitations of the t-test Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2. Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)

More information

Opgaven Onderzoeksmethoden, Onderdeel Statistiek

Opgaven Onderzoeksmethoden, Onderdeel Statistiek Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week

More information

Is it statistically significant? The chi-square test

Is it statistically significant? The chi-square test UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical

More information

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.

More information

Two-sample hypothesis testing, II 9.07 3/16/2004

Two-sample hypothesis testing, II 9.07 3/16/2004 Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,

More information

Chi Square Distribution

Chi Square Distribution 17. Chi Square A. Chi Square Distribution B. One-Way Tables C. Contingency Tables D. Exercises Chi Square is a distribution that has proven to be particularly useful in statistics. The first section describes

More information

Chapter 8. Hypothesis Testing

Chapter 8. Hypothesis Testing Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing

More information

Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS

Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS About Omega Statistics Private practice consultancy based in Southern California, Medical and Clinical

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1 Unit 2 Review Name Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 1) Miles (per day) 1-2 9 3-4 22 5-6

More information

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHI-SQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chi-square tests of independence we use the hypotheses. H0: The variables are independent

More information

Math 251, Review Questions for Test 3 Rough Answers

Math 251, Review Questions for Test 3 Rough Answers Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

More information

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative

More information

AP STATISTICS TEST #2 - REVIEW - Ch. 14 &15 Period:

AP STATISTICS TEST #2 - REVIEW - Ch. 14 &15 Period: AP STATISTICS Name TEST #2 - REVIEW - Ch. 14 &15 Period: 1) The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a committee, what is the probability these chairpersons

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96 1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

More information

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous Chapter 2 Overview Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify as categorical or qualitative data. 1) A survey of autos parked in

More information

Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for

More information

Hypothesis Testing: Two Means, Paired Data, Two Proportions

Hypothesis Testing: Two Means, Paired Data, Two Proportions Chapter 10 Hypothesis Testing: Two Means, Paired Data, Two Proportions 10.1 Hypothesis Testing: Two Population Means and Two Population Proportions 1 10.1.1 Student Learning Objectives By the end of this

More information

5) The table below describes the smoking habits of a group of asthma sufferers. two way table ( ( cell cell ) (cell cell) (cell cell) )

5) The table below describes the smoking habits of a group of asthma sufferers. two way table ( ( cell cell ) (cell cell) (cell cell) ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine which score corresponds to the higher relative position. 1) Which score has a better relative

More information

Confidence Intervals

Confidence Intervals Section 6.1 75 Confidence Intervals Section 6.1 C H A P T E R 6 4 Example 4 (pg. 284) Constructing a Confidence Interval Enter the data from Example 1 on pg. 280 into L1. In this example, n > 0, so the

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

More information

Chi-square (χ 2 ) Tests

Chi-square (χ 2 ) Tests Math 442 - Mathematical Statistics II May 5, 2008 Common Uses of the χ 2 test. 1. Testing Goodness-of-fit. Chi-square (χ 2 ) Tests 2. Testing Equality of Several Proportions. 3. Homogeneity Test. 4. Testing

More information

Mind on Statistics. Chapter 13

Mind on Statistics. Chapter 13 Mind on Statistics Chapter 13 Sections 13.1-13.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question

More information

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

Dawson College - Fall 2004 Mathematics Department

Dawson College - Fall 2004 Mathematics Department Dawson College - Fall 2004 Mathematics Department Final Examination Statistics (201-257-DW) No. Score Out of 1 8 2 10 3 8 Date: Thursday, December 16, 2004 Time: 9:30 12:30 Instructors: Kourosh A. Zarabi

More information

Chapter 5 - Practice Problems 1

Chapter 5 - Practice Problems 1 Chapter 5 - Practice Problems 1 Identify the given random variable as being discrete or continuous. 1) The number of oil spills occurring off the Alaskan coast 1) A) Continuous B) Discrete 2) The ph level

More information

Solutions to Worksheet on Hypothesis Tests

Solutions to Worksheet on Hypothesis Tests s to Worksheet on Hypothesis Tests. A production line produces rulers that are supposed to be inches long. A sample of 49 of the rulers had a mean of. and a standard deviation of.5 inches. The quality

More information

8 6 X 2 Test for a Variance or Standard Deviation

8 6 X 2 Test for a Variance or Standard Deviation Section 8 6 x 2 Test for a Variance or Standard Deviation 437 This test uses the P-value method. Therefore, it is not necessary to enter a significance level. 1. Select MegaStat>Hypothesis Tests>Proportion

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Mind on Statistics. Chapter 4

Mind on Statistics. Chapter 4 Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

More information

Name: (b) Find the minimum sample size you should use in order for your estimate to be within 0.03 of p when the confidence level is 95%.

Name: (b) Find the minimum sample size you should use in order for your estimate to be within 0.03 of p when the confidence level is 95%. Chapter 7-8 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. Please indicate which program

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

More information

AP Statistics 2013 Free-Response Questions

AP Statistics 2013 Free-Response Questions AP Statistics 2013 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in

More information

AP STATISTICS (Warm-Up Exercises)

AP STATISTICS (Warm-Up Exercises) AP STATISTICS (Warm-Up Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,

More information

1. A survey of a group s viewing habits over the last year revealed the following

1. A survey of a group s viewing habits over the last year revealed the following 1. A survey of a group s viewing habits over the last year revealed the following information: (i) 8% watched gymnastics (ii) 9% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

Mind on Statistics. Chapter 2

Mind on Statistics. Chapter 2 Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table

More information

2 Tests for Goodness of Fit:

2 Tests for Goodness of Fit: Tests for Goodness of Fit: General Notion: We often wish to know whether a particular distribution fits a general definition Example: To use t tests, we must suppose that the population is normally distributed

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution

More information

Module 2 Probability and Statistics

Module 2 Probability and Statistics Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

More information

12.5: CHI-SQUARE GOODNESS OF FIT TESTS

12.5: CHI-SQUARE GOODNESS OF FIT TESTS 125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability

More information

Basic Statistics Self Assessment Test

Basic Statistics Self Assessment Test Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A soda-dispensing machine fills 12-ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation

More information

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test

More information

In the past, the increase in the price of gasoline could be attributed to major national or global

In the past, the increase in the price of gasoline could be attributed to major national or global Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null

More information

BLS SPOTLIGHT ON STATISTICS SPORTS AND EXERCISE

BLS SPOTLIGHT ON STATISTICS SPORTS AND EXERCISE Sports and Exercise May 2008 What percentage of people (aged 15 years and older) who live in the United States participated in sports and exercise activities on an average day in recent years? About 16

More information

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0. Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.

More information

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph. MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

More information

Hypothesis Testing Exercises-Printable Page 1 of 7

Hypothesis Testing Exercises-Printable Page 1 of 7 Hypothesis Testing Exercises-Printable Page 1 of 7 BioEpi 540 Home > Topics > Hypothesis Testing > Exercises Topics Hypothesis Testing Exercises (to print: pdf 35k 7 pages) HT1. [Solution pdf 101k 4 pages

More information

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions.

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

More information

Hypothesis Testing Population Mean

Hypothesis Testing Population Mean Z-test About One Mean ypothesis Testing Population Mean The Z-test about a mean of population we are using is applied in the following three cases: a. The population distribution is normal and the population

More information

Elementary Statistics

Elementary Statistics lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page

More information

HYPOTHESIS TESTING: POWER OF THE TEST

HYPOTHESIS TESTING: POWER OF THE TEST HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,

More information

Hypothesis Testing --- One Mean

Hypothesis Testing --- One Mean Hypothesis Testing --- One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis

More information

statistics Chi-square tests and nonparametric Summary sheet from last time: Hypothesis testing Summary sheet from last time: Confidence intervals

statistics Chi-square tests and nonparametric Summary sheet from last time: Hypothesis testing Summary sheet from last time: Confidence intervals Summary sheet from last time: Confidence intervals Confidence intervals take on the usual form: parameter = statistic ± t crit SE(statistic) parameter SE a s e sqrt(1/n + m x 2 /ss xx ) b s e /sqrt(ss

More information

University of Chicago Graduate School of Business. Business 41000: Business Statistics

University of Chicago Graduate School of Business. Business 41000: Business Statistics Name: University of Chicago Graduate School of Business Business 41000: Business Statistics Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper for the formulas. 2. Throughout

More information

Additional Probability Problems

Additional Probability Problems Additional Probability Problems 1. A survey has shown that 52% of the women in a certain community work outside the home. Of these women, 64% are married, while 86% of the women who do not work outside

More information

9 Testing the Difference

9 Testing the Difference blu49076_ch09.qxd 5/1/2003 8:19 AM Page 431 c h a p t e r 9 9 Testing the Difference Between Two Means, Two Variances, and Two Proportions Outline 9 1 Introduction 9 2 Testing the Difference Between Two

More information

Elementary Statistics

Elementary Statistics Elementary Statistics Chapter 1 Dr. Ghamsary Page 1 Elementary Statistics M. Ghamsary, Ph.D. Chap 01 1 Elementary Statistics Chapter 1 Dr. Ghamsary Page 2 Statistics: Statistics is the science of collecting,

More information

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.

Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures. Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

More information

Practice Problems and Exams

Practice Problems and Exams Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 2009-2010

More information

MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6

MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6 MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/6 "Pepsi" problem A market research consultant hired by the Pepsi-Cola Co. is interested

More information

Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED

Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chi-square test to use. You will input data into a list or matrix and conduct

More information

Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish

Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Statistics Statistics are quantitative methods of describing, analysing, and drawing inferences (conclusions)

More information

Practice Midterm Exam #2

Practice Midterm Exam #2 The Islamic University of Gaza Faculty of Engineering Department of Civil Engineering 12/12/2009 Statistics and Probability for Engineering Applications 9.2 X is a binomial random variable, show that (

More information

Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means) Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

More information

THE LOGIC OF HYPOTHESIS TESTING. The general process of hypothesis testing remains constant from one situation to another.

THE LOGIC OF HYPOTHESIS TESTING. The general process of hypothesis testing remains constant from one situation to another. THE LOGIC OF HYPOTHESIS TESTING Hypothesis testing is a statistical procedure that allows researchers to use sample to draw inferences about the population of interest. It is the most commonly used inferential

More information

AP Statistics Chapters 11-12 Practice Problems MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Statistics Chapters 11-12 Practice Problems MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. AP Statistics Chapters 11-12 Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Criticize the following simulation: A student

More information

3. There are three senior citizens in a room, ages 68, 70, and 72. If a seventy-year-old person enters the room, the

3. There are three senior citizens in a room, ages 68, 70, and 72. If a seventy-year-old person enters the room, the TMTA Statistics Exam 2011 1. Last month, the mean and standard deviation of the paychecks of 10 employees of a small company were $1250 and $150, respectively. This month, each one of the 10 employees

More information

Solutions to Homework 10 Statistics 302 Professor Larget

Solutions to Homework 10 Statistics 302 Professor Larget s to Homework 10 Statistics 302 Professor Larget Textbook Exercises 7.14 Rock-Paper-Scissors (Graded for Accurateness) In Data 6.1 on page 367 we see a table, reproduced in the table below that shows the

More information

Statistics Review PSY379

Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

More information

Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific

Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin. You

More information

II. DISTRIBUTIONS distribution normal distribution. standard scores

II. DISTRIBUTIONS distribution normal distribution. standard scores Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

More information