Chi-Square Analysis
True/False
1. In a chi-square goodness-of-fit test theoretical frequencies are also called expected frequencies.
Ans:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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 0 1 2 3 4 5
Observed 47 56 39 22 18 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:
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 0 1 2 3 4 5
Observed 47 56 39 22 18 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:
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:
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 0 1 2 3 4 >5
Observed 7 18 25 17 12 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:
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 >5
Observed Frequency 5 15 17 12 10 8
The number of degrees of freedom for this goodness-of-fit test is _______.
a) 5
b) 4
c) 3
d) 2
e) 1
Ans:
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 0 1 2 3 4 >5
Observed Frequency 5 15 17 12 10 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:
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 0 1 2 3 4 >5
Observed Frequency 5 15 17 12 10 8
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:
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
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 0 1 2 3 4 >5
Observed Frequency 5 15 17 12 10 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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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’.
C D E
A 12 10 8
B 20 24 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:
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’.
C D E
A 12 10 8
B 20 24 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:
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’.
C D E
A 12 10 8
B 20 24 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:
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 households employment classification. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification
Clerical Managerial Professional
Subscribes Yes 10 90 60
No 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:
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 households employment classification. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification
Clerical Managerial Professional
Subscribes Yes 10 90 60
No 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:
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 households employment classification. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification
Clerical Managerial Professional
Subscribes Yes 10 90 60
No 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:
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 households employment classification. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification
Clerical Managerial Professional
Subscribes Yes 10 90 60
No 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:
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.
Children in Household
Pre-teenagers teenagers none
Preferred Package Pump 30 20 10
Tube 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:
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.
Children in Household
Pre-teenagers teenagers none
Preferred Package Pump 30 20 10
Tube 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:
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.
Children in Household
Pre-teenagers teenagers none
Preferred Package Pump 30 20 10
Tube 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:
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.
Children in Household
Pre-teenagers teenagers none
Preferred Package Pump 30 20 10
Tube 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:
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 Industry Sector
Objective Electronics Airlines Healthcare
Growth 100 10 40
Income 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:
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 Industry Sector
Objective Electronics Airlines Healthcare
Growth 100 10 40
Income 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:
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 Industry Sector
Objective Electronics Airlines Healthcare
Growth 100 10 40
Income 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:
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 Industry Sector
Objective Electronics Airlines Healthcare
Growth 100 10 40
Income 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:
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 Industry Sector
Objective Electronics Airlines Healthcare
Growth 100 10 40
Income 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:
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
70. A gasoline distributor wonders whether an individuals income level influences the grade of gasoline purchased.
Personal Type of Gasoline
Income Regular Premium Extra Premium
Less than $30000 90 10 20
$30000 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:
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
71. A gasoline distributor wonders whether an individuals income level influences the grade of gasoline purchased.
Pers

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