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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

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