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File: Ch16, Chapter 16: Chi-Square Analysis True/False 1. In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 2. In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies. Ans: False Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 3. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated. Ans: False Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 4. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 5. A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a normal distribution (the mean and the standard deviation of which must be estimated) for a data with "k" categories. This test has (k-3) degrees of freedom. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 6. The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 7. The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 8. When using the chi-square goodness-of-fit test, we must make sure that none of the expected frequencies is less than 30. Ans: False Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 9. A chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom. Ans: True Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 10. A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom. Ans: False Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 11. A two-way table used for a test of independence is sometimes called a contingency table. Ans: True Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 12. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 12. Ans: False Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 13. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 7. Ans: False Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 14. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 6. Ans: True Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 15. The null hypothesis for a chi-square test of independence is that the two variables are not related. Ans: True Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy Multiple Choice 16. A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C) more than the other two. A sample of 60 consumers is used. What is the expected frequency for category A? a) 1/3 b) 20 c) 60 d) 10 e) 30 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 17. A goodness of fit test is to be performed to see if Web Surfers prefer any of four Web sites (A, B, C and D) more than the other three. A sample of 60 consumers is used. What is the expected frequency for Web site A? a) 1/4 b) 20 c) 15 d) 10 e) 30 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 18. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using = .01, the degrees of freedom for this test are _______. a) 5 b) 4 c) 3 d) 2 e) 1 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 19. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using = .01, the critical value of chi-square is _______. a) 7.78 b) 15.09 c) 9.24 d) 13.28 e) 15.48 Ans: d Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 20. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using = .01, the observed value of chi-square is _______. a) 12.09 b) 9.82 c) 13.28 d) 17.81 e) 2.09 Ans: e Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Middle 21. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using = .01, the appropriate decision is _______. a) reject the null hypothesis that the observed distribution is uniform b) reject the null hypothesis that the observed distribution is not uniform c) do not reject the null hypothesis that the observed distribution is uniform d) do not reject the null hypothesis that the observed distribution is not uniform e) do nothing Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 22. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using = .01, the critical chi-square value is _______. a) 13.277 b) 15.086 c) 7.779 d) 11.070 e) 14.356 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 23. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using = .01, the observed chi-square value is _______. a) 1.18 b) 9.10 c) 20.27 d) 4.51 e) 19.70 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 24. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using = .01, the appropriate decision is _______. a) do not reject the null hypothesis that the observed distribution is uniform b) do not reject the null hypothesis that the observed distribution is not uniform c) reject the null hypothesis that the observed distribution is uniform d) reject the null hypothesis that the observed distribution is not uniform e) do nothing Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 25. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using = .10, the appropriate decision is _______. a) do not reject the null hypothesis that the observed distribution is uniform b) do not reject the null hypothesis that the observed distribution is not uniform c) reject the null hypothesis that the observed distribution is uniform d) reject the null hypothesis that the observed distribution is not uniform e) do nothing Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 26. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using = .05, the critical chi-square value is _______. a) 13.277 b) 15.086 c) 7.8147 d) 11.070 e) 15.546 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 27. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using = .05, the observed chi-square value is _______. a) 5.418 b) 9.10 c) 20.27 d) 4.51 e) 7.86 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 28. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using = .05, the appropriate decision is _______. a) do not reject the null hypothesis that the observed distribution is uniform b) do not reject the null hypothesis that the observed distribution is not uniform c) reject the null hypothesis that the observed distribution is uniform d) reject the null hypothesis that the observed distribution is not uniform e) do nothing Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 29. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using = .10, the appropriate decision is _______. a) do not reject the null hypothesis that the observed distribution is uniform b) do not reject the null hypothesis that the observed distribution is not uniform c) reject the null hypothesis that the observed distribution is uniform d) reject the null hypothesis that the observed distribution is not uniform e) do nothing Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 30. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 6 categories, and lambda must be estimated. How many degrees of freedom should be used? a) 6 b) 5 c) 4 d) 3 e) 2 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 31. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. How many degrees of freedom should be used? a) 8 b) 7 c) 6 d) 5 e) 4 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 32. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. Alpha is chosen to be 0.10. The critical (table) value of chi-square is _______. a) 10.645 b) 12.017 c) 3.828 d) 16.812 e) 17.345 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 33. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Category Observed 0 47 1 56 2 39 3 22 4 18 5 10 Using = 0.10, the critical chi-square value for this goodness-of-fit test is _______. a) 1.064 b) 13.277 c) 9.236 d) 8.799 e) 7.779 Ans: e Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 34. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Category Observed 0 47 1 56 2 39 3 22 4 18 5 10 Using = 0.10, the observed chi-square value for this goodness-of-fit test is ____. a) 2.28 b) 14.56 c) 17.43 d) 1.68 e) 2.67 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 35. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Category 0 1 2 3 4 >5 Observed 7 18 25 17 12 5 Using = 0.10, the critical value of chi-square for the data is _______. a) 9.236 b) 7.779 b) 1.064 c) 13.277 d) 12.89 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 36. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Category Observed 0 7 1 18 2 25 3 17 4 12 >5 5 Using = 0.10, the value of the observed chi-square for the data is _______. a) 19.37 b) 2.29 c) 1.74 d) 3.28 e) 4.48 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 37. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15 minute interval 0 1 2 3 4 Observed Frequency 5 15 17 12 10 The number of degrees of freedom for this goodness-of-fit test is _______. a) 5 b) 4 c) 3 >5 8 d) 2 e) 1 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 38. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15 minute interval Observed Frequency 0 5 1 15 2 17 3 12 4 10 >5 8 Using = 0.05, the critical value of chi-square for this goodness-of-fit test is ____. a) 9.49 b) 7.81 c) 7.78 d) 11.07 e) 12.77 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 39. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15 minute interval Observed Frequency 0 5 1 15 2 17 3 12 The observed value of chi-square for this goodness-of-fit test is _____. a) 0.73 b) 6.72 c) 3.15 d) 7.81 e) 9.87 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test 4 10 >5 8 Difficulty: Hard 40. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15 minute interval Observed Frequency 0 5 1 15 2 17 3 12 4 10 >5 8 Using = 0.05, the appropriate decision for this goodness-of-fit test is ____. a) reject the null hypothesis that the observed distribution is Poisson b) reject the null hypothesis that the observed distribution is not Poisson c) do not reject the null hypothesis that the observed distribution is not Poisson d) do not reject the null hypothesis that the observed distribution is Poisson e) do nothing Ans: d Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Hard 41. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is: "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______. a) p > 0.05 b) p = 0.05 c) 30 d) > 30 e) s > 30 Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 42. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.01, critical chi-square value is _______. a) 6.63 b) 9.21 c) 7.88 d) 10.60 e) 12.34 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 43. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.01, observed chi-square value is _______. a) 13.38 b) 26.29 c) 2.09 d) 1.05 e) 3.98 Ans: d Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 44. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.01, the appropriate decision is _______. a) reject the null hypothesis p > 0.05 b) do not reject the null hypothesis p = 0.05 c) reject the null hypothesis > 30 d) do not reject the null hypothesis 30 e) do nothing Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 45. The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian. Using = 0.05, the null hypothesis is __________. a) > 80 b) 80 c) p > 0.50 d) p = 0.50 e) s ≥ 0.80 Ans: d Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 46. The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian. Using = 0.05, the critical value of chi-square is _______. a) 7.38 b) 5.02 c) 3.84 d) 5.99 e) 6.99 Ans: c Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Easy 47. The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian. Using = 0.05, the observed value of chi-square is __________. a) 8.00 b) 2.82 c) 4.00 d) 9.71 e) 9.97 Ans: a Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 48. The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian. Using = 0.05, the appropriate decision is ________. a) do not reject the null hypothesis p > 0.50 b) reject the null hypothesis p = 0.50 c) reject the null hypothesis > 80 d) do not reject the null hypothesis 80 e) do nothing Ans: b Response: See section 16.1 Chi-Square Goodness-of-Fit Test Difficulty: Medium 49. A test of independence is to be performed. The contingency table has 4 rows and 5 columns. What would the degrees of freedom be? a) 20 b) 9 c) 7 d) 12 e) 19 Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 50. A contingency table is to be used to test for independence. There are 3 rows and 3 columns in the table. How many degrees of freedom are there for this problem? a) 6 b) 5 c) 4 d) 3 e) 1 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 51. A contingency table has five rows and six columns. When applying a chi-square test of independence to this table, the number of degrees of freedom is _____. a) 9 b) 20 c) 30 d) 11 e) 12 Ans: b Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 52. A contingency table has seven rows and five columns. When applying a chi-square test of independence to this table, the number of degrees of freedom is _____. a) 24 b) 35 c) 12 d) 10 e) 11 Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 53. Contingency tables should not be used with expected cell frequencies _______. a) less than the number of rows b) less than the number of columns c) less than 5 d) less than 30 e) less than 50 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 54. Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. A B C 12 20 D 10 24 E 8 26 Using = 0.05, the critical chi-square value is _______. a) 9.488 b) 1.386 c) 8.991 d) 3.357 e) 5.991 Ans: e Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 55. Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. A B C 12 20 D 10 24 E 8 26 Using = 0.05, the observed chi-square value is _______. a) 0 b) 0.69 c) 1.54 d) 21.28 e) 8.29 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium 56. Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. A B C 12 20 D 10 24 E 8 26 Using = 0.05, the expected frequency in row 1 (A) column 1 (C) is _______. a) 9.6 b) 12 c) 16 d) 10 e) 20 Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 57. Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine. He wonders whether subscriptions are influenced by the head of household’s employment classification. His staff prepared the following contingency table from a random sample of 300 households. Subscribes Yes No Head of Household Classification Clerical Managerial Professional 10 90 60 60 60 20 Sam's null hypothesis is ______________. a) "head of household classification" is related to "subscribes" b) "head of household classification" is not independent of "subscribes" c) "head of household classification" is independent of "subscribes” d) "head of household classification" influences "subscribes" e) “clerical is not related to managerial” Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 58. Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine. He wonders whether subscriptions are influenced by the head of household’s employment classification. His staff prepared the following contingency table from a random sample of 300 households. Subscribes Yes No Head of Household Classification Clerical Managerial Professional 10 90 60 60 60 20 Using = .05, the critical value of chi-square is ______________. a) 5.99 b) 3.84 c) 5.02 d) 7.37 e) 9.99 Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 59. Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine. He wonders whether subscriptions are influenced by the head of household’s employment classification. His staff prepared the following contingency table from a random sample of 300 households. Subscribes Yes No Head of Household Classification Clerical Managerial Professional 10 90 60 60 60 20 The observed value of chi-square is ______________. a) 5.99 b) 28.30 c) 32.35 d) 60.65 e) 50.78 Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium 60. Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine. He wonders whether subscriptions are influenced by the head of household’s employment classification. His staff prepared the following contingency table from a random sample of 300 households. Subscribes Yes No Head of Household Classification Clerical Managerial Professional 10 90 60 60 60 20 Using = .05, the appropriate decision is ______________. a) reject the null hypothesis and conclude the two variables are independent b) do not reject the null hypothesis and conclude the two variables are independent c) reject the null hypothesis and conclude the two variables are not independent d) do not reject the null hypothesis and conclude the two variables are not independent e) do nothing Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: High 61. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households. Preferred Package Pump Tube Children in Household Pre-teenagers teenagers none 30 20 10 10 10 20 Catherine's null hypothesis is ______________. a) "children in household" is not independent of "preferred package" b) "children in household" is independent of "preferred package" c) "children in household" is related to "preferred package" d) "children in household" influences "preferred package" e) “pump” is independent of “tube” Ans: b Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 62. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households. Preferred Package Pump Tube Children in Household Pre-teenagers teenagers none 30 20 10 10 10 20 Using = .05, the critical value of chi-square is ______________. a) 5.02 b) 3.84 c) 7.37 d) 6.09 e) 5.99 Ans: e Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 63. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households. Preferred Package Pump Tube Children in Household Pre-teenagers teenagers none 30 20 10 10 10 20 Using = .05, the observed value of chi-square is ______________. a) 5.28 b) 9.49 c) 13.19 d) 16.79 e) 18.79 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium 64. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households. Preferred Package Pump Tube Children in Household Pre-teenagers teenagers none 30 20 10 10 10 20 Using = .05, the appropriate decision is ______________. a) reject the null hypothesis and conclude the two variables are not independent b) do not reject the null hypothesis and conclude the two variables are not independent c) reject the null hypothesis and conclude the two variables are independent d) do not reject the null hypothesis and conclude the two variables are independent e) do nothing Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Hard 65. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks. Investment Objective Growth Income Industry Sector Electronics Airlines Healthcare 100 10 40 20 20 10 Anita's null hypothesis is ______________. a) "investment objective" is related to "industry sector" b) "investment objective" influences "industry sector" c) "investment objective" is not independent of "industry sector" d) "investment objective" is independent of "industry sector" e) “growth” and “income” are independent Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 66. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks. Investment Objective Growth Income Industry Sector Electronics Airlines Healthcare 100 10 40 20 20 10 Using = .01, critical chi-square value is ______________. a) 9.21 b) 7.88 c) 15.09 d) 16.81 e) 18.81 Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 67. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks. Investment Objective Growth Income Industry Sector Electronics Airlines Healthcare 100 10 40 20 20 10 Using = .05, critical chi-square value is ______________. a) 9.21 b) 7.88 c) 15.09 d) 5.99 e) 7.89 Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 68. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks. Investment Objective Growth Income Industry Sector Electronics Airlines Healthcare 100 10 40 20 20 10 Using = .01, observed chi-square value is ______________. a) 24.93 b) 8.17 c) 32.89 d) 6.59 e) 4.89 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 69. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks. Investment Objective Growth Income Industry Sector Electronics Airlines Healthcare 100 10 40 20 20 10 Using = .01, appropriate decision is ______________. a) reject the null hypothesis and conclude the two variables are not independent b) reject the null hypothesis and conclude the two variables are independent c) do not reject the null hypothesis and conclude the two variables are not independent d) do not reject the null hypothesis and conclude the two variables are independent e) do nothing Ans: b Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Hard 70. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 90 10 20 $30,000 or More 60 60 60 The null hypothesis is ______________. a) "income” is independent of "type of gasoline” b) "income” influences "type of gasoline” c) "income” is not independent of "type of gasoline” d) “income" is related to "type of gasoline" e) “regular” is independent of “premium” Ans: a Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 71. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 90 10 20 $30,000 or More 60 60 60 Using = .01, critical chi-square value is ______________. a) 15.09 b) 7.88 c) 9.21 d) 16.81 e) 17.89 Ans: c Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 72. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 90 10 20 $30,000 or More 60 60 60 Using = .01, observed chi-square value is ______________. a) 24.93 b) 4.44 c) 32.89 d) 51.79 e) 54.98 Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium 73. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 80 30 30 $30,000 or More 70 40 50 Using = .05, critical chi-square value is ______________. a) 15.09 b) 5.99 c) 9.21 d) 16.81 e) 23.87 Ans: b Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy 74. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 80 30 30 $30,000 or More 70 40 50 Using = .05, observed chi-square value is ______________. a) 15.79 b) 4.44 c) 32.89 d) 51.79 e) 5.79 Ans: e Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium 75. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. Personal Type of Gasoline Income Regular Premium Extra Premium Less than $30,000 80 30 30 $30,000 or More 70 40 50 Using = .05, appropriate decision is ______________. a) reject the null hypothesis and conclude the two variables are not independent b) reject the null hypothesis and conclude the two variables are independent c) do not reject the null hypothesis and conclude the two variables are not independent d) do not reject the null hypothesis and conclude the two variables are independent e) do nothing Ans: d Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: High