Ch16 Test Bank Analysis Of Categorical Data - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: Ch16, Chapter 16: Analysis of Categorical Data
True/False
1. In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
2. In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
5. A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories. This test has (k-3) degrees of freedom.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
6. The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
7. The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square value is greater than the table chi-square value.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
8. When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal) being used does not influence the hypothesis test.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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.
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
11. A two-way table used for a test of independence is sometimes called a contingency table.
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
12. A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading. Age is divided into four categories while minutes spent reading is classified as high, medium, low. The number of degrees of freedom for this test is 12.
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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.
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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.
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
15. The null hypothesis for a chi-square test of independence is that the two variables are not related.
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
22. A suburban realtor is studying commuter time in the Houston metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies 9 days, 15 days, 8 days, 11 days, 12 days. Using = .01, the critical chi-square value is _______.
a) 13.277
b) 15.086
c) 7.779
d) 11.070
e) 2.727
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
23. A suburban realtor is studying commuter time in the Houston metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am. She expects that data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies 9 days, 15 days, 8 days, 11 days, 12 days. Using = .01, the observed chi-square value is _______.
a) 1.18
b) 9.10
c) 21.75
d) 4.51
e) 2.73
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
24. A suburban realtor is studying commuter time in the Houston metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies 9 days, 15 days, 8 days, 11 days, 12 days. 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
25. A suburban realtor is studying commuter time in the Houston metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies 9 days, 15 days, 8 days, 11 days, 12 days. 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
26. A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
27. A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
28. A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
29. A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
33. A researcher believes that arrivals at a walk-in hair salon are Poisson distributed. The following data represent a distribution of frequency of arrivals in a one-hour time period.
Number of customer arrivals | 0 | 1 | 2 | 3 | 4 | ≥5 |
Frequency | 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
34. A researcher believes that arrivals at a walk-in hair salon are Poisson distributed. The following data represent a distribution of frequency of arrivals in a one hour time period.
Number of Customer Arrivals | 0 | 1 | 2 | 3 | 4 | ≥5 |
Frequency | 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) 14.82
c) 17.43
d) 1.68
e) 2.67
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
37. Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
38. Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
39. Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows 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 closest to _____.
a) 0.73
b) 6.72
c) 3.15
d) 7.81
e) 9.87
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
40. Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows 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
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Hard
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
41. The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution. While watching the lane at random times throughout the day and week, she collects the following information.
People waiting in express check out lane | 0 | 1 | 2 | 3 | 4 | >5 |
Observed frequency | 35 | 41 | 22 | 14 | 3 | 2 |
Using α=0.10, the critical value of chi-square for this goodness of fit test is _______.
a) 9.49
b) 7.81
c) 7.78
d) 10.28
e) 11.41
Ans: c
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
42. The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution. While watching the lane at random times throughout the day and week, she collects the following information.
People waiting in express check out lane | 0 | 1 | 2 | 3 | 4 | >5 |
Observed frequency | 35 | 41 | 22 | 14 | 3 | 2 |
The observed value of chi-square for this goodness-of-fit test is closest to_______.
a) 0.99
b) 2.33
c) 4.54
d) 9.77
e) 13.05
Ans: b
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
43. The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution. While watching the lane at random times throughout the day and week, she collects the following information.
People waiting in express check out lane | 0 | 1 | 2 | 3 | 4 | >5 |
Observed frequency | 35 | 41 | 22 | 14 | 3 | 2 |
Using α=0.10, the appropriate decision for this goodness of fit test is _______.
a) do not reject the null hypothesis that the observed distribution is Poisson
b) reject the null hypothesis that the observed distribution is not the Poisson
c) do nothing
d) do not reject the null hypothesis that the observed distribution is not Poisson
e) reject the null hypothesis that the observed distribution is Poisson
Ans: a
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
44. In a college dining hall, students with a full meal plan can eat up to four meals each day. The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution. Reviewing dining hall data over the past week, the following information is compiled.
Meals | 0 | 1 | 2 | 3 | >4 |
Observed frequency | 287 | 581 | 447 | 290 | 185 |
Using α=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) 10.28
e) 11.41
Ans: b
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
45. In a college dining hall, students with a full meal plan can eat up to four meals each day. The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution. Reviewing dining hall data over the past week, the following information is compiled.
Meals | 0 | 1 | 2 | 3 | >4 |
Observed frequency | 287 | 581 | 447 | 290 | 185 |
The observed value of chi-square for this goodness-of-fit test is closest to _______.
a) 1.54
b) 4.88
c) 4.97
d) 8.49
e) 11.27
Ans: e
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
46. In a college dining hall, students with a full meal plan can eat up to four meals each day. The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution. Reviewing dining hall data over the past week, the following information is compiled.
Meals | 0 | 1 | 2 | 3 | >4 |
Observed frequency | 287 | 581 | 447 | 290 | 185 |
Using α=0.05, the appropriate decision for this goodness of fit test is _______.
a) do not reject the null hypothesis that the observed distribution is Poisson
b) reject the null hypothesis that the observed distribution is not the Poisson
c) do nothing
d) do not reject the null hypothesis that the observed distribution is not Poisson
e) reject the null hypothesis that the observed distribution is Poisson
Ans: e
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
47. In a college dining hall, students with a full meal plan can eat up to four meals each day. The kitchen is now thinking that the meal consumption may more closely resemble a uniform distribution. Reviewing dining hall data over the past week, the following information is compiled.
Meals | 0 | 1 | 2 | 3 | >4 |
Observed frequency | 287 | 581 | 447 | 290 | 185 |
Using α=0.05, the appropriate decision for this goodness of fit test is _______.
a) do not reject the null hypothesis that the observed distribution is uniform
b) reject the null hypothesis that the observed distribution is uniform
c) do nothing
d) do not reject the null hypothesis that the observed distribution is not uniform
e) reject the null hypothesis that the observed distribution is not uniform
Ans: b
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension
48. The chi-square test of independence uses the _______ of two categorical variables to determine whether those variables are independent.
a) number of categories
b) frequencies
c) means
d) standard deviations
e) total counts
Ans: b
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
49. The type of data most appropriate for use in the chi-square test of independence is ______.
a) ratio
b) interval
c) continuous
d) ordinal
e) nominal
Ans: e
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
50. 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
51. 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
52. A travel agent believes that vacation destinations are independent of the region of the country that the vacationer resides. She has compiled a table with six vacation destinations and five regions throughout the United States. 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
53. A market researcher believes that industry type is independent of the operating margin. He compiles a table with seven industry classifications and classifies operating margin into five levels. 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
54. 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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 critical chi-square value is _______.
a) 9.488
b) 1.386
c) 8.991
d) 3.357
e) 5.991
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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 observed chi-square value is _______.
a) 0
b) 0.69
c) 1.54
d) 21.28
e) 8.29
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Medium
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
57. 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 estimates of the expected frequency in row 1 (A) column 1 (C) when the two variables are independent is _______.
a) 9.6
b) 12
c) 16
d) 10
e) 20
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
58. Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household’s highest degree earned. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification | ||||
Associate | Bachelor | Master/ PhD | ||
Subscribers | 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”
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
59. Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household’s highest degree earned. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification | ||||
Associate | Bachelor | Master/ PhD | ||
Subscribers | 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
60. Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household’s highest degree earned. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification | ||||
Associate | Bachelor | Master/PhD | ||
Subscribers | 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Medium
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
61. Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household’s highest degree earned. His staff prepared the following contingency table from a random sample of 300 households.
Head of Household Classification | ||||
Associate | Bachelor | Master/ PhD | ||
Subscribers | 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
62. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by the age of the 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”
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
63. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by the age of the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
64. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by the age of the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Medium
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
65. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by the age of the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
66. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
67. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
68. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
69. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
70. Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether the 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
71. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 90 | 10 | 20 |
$50,000 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”
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
72. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 90 | 10 | 20 |
$50,000 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
73. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 90 | 10 | 20 |
$50,000 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Medium
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
74. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 80 | 30 | 30 |
$50,000 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
75. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 80 | 30 | 30 |
$50,000 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Medium
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
76. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 80 | 30 | 30 |
$50,000 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
77. A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals.
Personal | Type of Gasoline | ||
Income | Regular | Premium | Extra Premium |
Less than $50,000 | 90 | 10 | 20 |
$50,000 or More | 60 | 60 | 60 |
The estimate of the expected number of individuals with income less than $30,000 who purchase regular gasoline when income and type of gasoline are independent is _______.
a) 60
b) 90
c) 120
d )80
e) 100
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
78. A recent national poll showed the reading habits of adults during the last 12 months:
3 or more books | 5 | ||
2 books | 27 | ||
1 book | 38 | ||
No books |
|
| 30 |
A poll in a small Midwestern town shows the following percentages:
3 or more books | 1 | ||
2 books | 22 | ||
1 book | 39 | ||
No books |
|
| 38 |
The null hypothesis is: ______.
a) the poll in the small Midwestern town is not based on a random sample
b) the poll in the small Midwestern town is not accurate
c) the sample size for the poll in the Midwestern town is not large enough
d) the distributions are equal
e) the poll in the small Midwestern town is based on a random sample
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
79. A recent national poll showed the reading habits of adults during the last 12 months:
3 or more books | 5 | ||
2 books | 27 | ||
1 book | 38 | ||
No books |
|
| 30 |
A poll in a small Midwestern town shows the following percentages:
3 or more books | 1 | ||
2 books | 22 | ||
1 book | 39 | ||
No books |
|
| 38 |
The observed chi-squared statistic is ______.
a) 5.14
b) 5.28
c) 6.14
d) 6.28
e) 6.54
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
80. A recent national poll showed the reading habits of adults during the last 12 months:
3 or more books | 5 | ||
2 books | 27 | ||
1 book | 38 | ||
No books |
|
| 30 |
A poll in a small Midwestern town shows the following percentages:
3 or more books | 1 | ||
2 books | 22 | ||
1 book | 39 | ||
No books |
|
| 38 |
Using = .05, the critical value of the chi-squared goodness-of-fit statistic is ______.
a) 9.49
b) 7.82
c) 5.99
d) 5.82
e) 5.49
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
81. A recent national poll showed the reading habits of adults during the last 12 months:
3 or more books | 5 | ||
2 books | 27 | ||
1 book | 38 | ||
No books |
|
| 30 |
A poll in a small Midwestern town shows the following percentages:
3 or more books | 1 | ||
2 books | 22 | ||
1 book | 39 | ||
No books |
|
| 38 |
Comparing the critical and observed values of the goodness-of fit chi-squared statistic and
α = 0.05, the appropriate decision is ______.
a) reject the null hypothesis that the two distributions are equal
b) fail to reject the null hypothesis that the two distributions are unequal
c) reject the null hypothesis that the two distributions are unequal
d) fail to reject the null hypothesis that the two distributions are equal
e) reject the null hypothesis that the sample size for the smaller poll is large enough
Response: See section 16.1 Chi-Square Goodness-of-Fit Test
Difficulty: Medium
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 16.1: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
82. A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:
Style_1 | Style_2 | Style_3 | |
18–25 | 125 | 13 | 6 |
26–35 | 87 | 12 | 6 |
36–45 | 50 | 22 | 12 |
46+ | 12 | 25 | 15 |
The researcher uses α = 0.05. The observed chi-square value is ______.
a) 86.59
b) 88.64
c) 89.59
d) 89.64
e) 90.59
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
83. A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:
Style_1 | Style_2 | Style_3 | |
18–25 | 125 | 13 | 6 |
26–35 | 87 | 12 | 6 |
36–45 | 50 | 22 | 12 |
46+ | 12 | 25 | 15 |
The researcher uses α = 0.05. The critical chi-square value is ______.
a) 9.8
b) 10.9
c) 12.6
d) 15.5
e) 18.7
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
84. A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:
Style_1 | Style_2 | Style_3 | |
18–25 | 125 | 13 | 6 |
26–35 | 87 | 12 | 6 |
36–45 | 50 | 22 | 12 |
46+ | 12 | 25 | 15 |
The researcher uses α = 0.05. The number of degrees of freedom is ______.
a) 12
b) 11
c) 10
d) 9
e) 6
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
85. A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:
Style_1 | Style_2 | Style_3 | |
18–25 | 125 | 13 | 6 |
26–35 | 87 | 12 | 6 |
36–45 | 50 | 22 | 12 |
46+ | 12 | 25 | 15 |
The researcher uses α = 0.05. The 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
Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 16.2: Use the chi-square test of independence to perform contingency analysis.
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Business Stats Contemporary Decision 10e | Test Bank by Ken Black
By Ken Black