# 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

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 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

### 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

### 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

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### 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

### 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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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)

### 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.

### 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,

### 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

### 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

### 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,

### 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

### 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

### 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

### 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

### 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

### 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

### Descriptive Statistics

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

### 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

### 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

### 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

### 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

### 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

### 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

### Section 8-1 Pg. 410 Exercises 12,13

Section 8- Pg. 4 Exercises 2,3 2. Using the z table, find the critical value for each. a) α=.5, two-tailed test, answer: -.96,.96 b) α=., left-tailed test, answer: -2.33, 2.33 c) α=.5, right-tailed test,

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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,

### 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

### 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

### 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,

### 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

### 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

### 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

### 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.

### 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

### 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

### 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.

### 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

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

### 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

### 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

### 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

### 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?

### 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,

### Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses

Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the

### 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

### 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

### 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,

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

### 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

### 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

### Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

### 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 (

### 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

### Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

### CHAPTER 15 NOMINAL MEASURES OF CORRELATION: PHI, THE CONTINGENCY COEFFICIENT, AND CRAMER'S V

CHAPTER 15 NOMINAL MEASURES OF CORRELATION: PHI, THE CONTINGENCY COEFFICIENT, AND CRAMER'S V Chapters 13 and 14 introduced and explained the use of a set of statistical tools that researchers use to measure

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

Exam Name 1) A recent report stated ʺBased on a sample of 90 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company -hired truck drivers.ʺ Does

### 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)

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### 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

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

STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

### SAMPLING DISTRIBUTIONS

0009T_c07_308-352.qd 06/03/03 20:44 Page 308 7Chapter SAMPLING DISTRIBUTIONS 7.1 Population and Sampling Distributions 7.2 Sampling and Nonsampling Errors 7.3 Mean and Standard Deviation of 7.4 Shape of

### Chi-square test Fisher s Exact test

Lesson 1 Chi-square test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions

### Research Methods & Experimental Design

Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and

### 3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

### 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

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### Assessment For The California Mathematics Standards Grade 6

Introduction: Summary of Goals GRADE SIX By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative

### Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to