Analysis of Categorical Data Exam Questions Black Ch.16 - Business Statistics 3e Canada -Test Bank by Ken Black. DOCX document preview.
CHAPTER 16
ANALYSIS OF CATEGORICAL DATA
CHAPTER LEARNING OBJECTIVES
1. Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension. Categorical data are non-numerical data that can be summarized as frequency counts of one or more categories. For example, business can be categorized into small, medium, or large. Chi-square tests analyze categorical data. The two techniques presented for analyzing categorical data are the chi-square goodness-of-fit test and the chi-square test of independence. These techniques are an outgrowth of the binomial distribution and the inferential techniques for analyzing population proportions.
The chi-square goodness-of-fit test is used to compare a theoretical or expected distribution of measurements for several categories of a variable with the actual or observed distribution of measurements. It can be used to determine whether a distribution of values fits a given distribution, such as the Poisson or normal distribution. If only two categories are used, the test offers the equivalent of a z test for a single proportion.
2. Use the chi-square test of independence to perform contingency analysis. The chi-square test of independence is used to analyze frequencies for categories of two variables to determine whether the two variables are independent. The data used in analysis by a chi-square test of independence are arranged in a two-dimensional table called a contingency table. For this reason, the test is sometimes referred to as contingency analysis. A chi-square test of independence is computed in a manner similar to that used with the chi-square goodness-of-fit test. Expected values are computed for each cell of the contingency table and then compared with observed values using the chi-square statistic.
Both the chi-square test of independence and the chi-square goodness-of-fit test require that expected values be greater than or equal to 5.
TRUE-FALSE STATEMENTS
1. In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
2. In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
6. The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is same as the expected distribution.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
8. When using the chi-square goodness-of-fit test, we must make sure that none of the expected frequencies is less than 30.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
9. A chi-square goodness-of-fit test to determine if the observed frequencies in eight categories are uniformly distributed has seven degrees of freedom.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Knowledge
AACSB: Reflective Thinking
11. A two-way table used for a test of independence is sometimes called a contingency table.
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
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.
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
15. The null hypothesis for a chi-square test of independence is that the two variables are not related.
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
MULTIPLE CHOICE QUESTIONS
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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
17. A goodness-of-fit test is to be performed to see if web surfers prefer any of four websites (A, B, C, and D) more than the other three. A sample of 60 consumers is used. What is the expected frequency for website A?
a) 1/4
b) 20
c) 15
d) 10
e) 30
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
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) 13.278
b) 15.086
c) 7.779
d) 11.070
e) 14.356
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Reflective Thinking
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Reflective Thinking
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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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) 14.57
c) 17.43
d) 1.68
e) 2.67
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
36. Sami Wilson believes that number of cars arriving at his Spotless 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
37. Sami Wilson believes that number of cars arriving at his Spotless 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
38. Sami Wilson believes that number of cars arriving at his Spotless 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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
39. Sami Wilson believes that number of cars arriving at his Spotless 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
Difficulty: Hard
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
40. Ophelia McPhee, VP of Consumer Credit, Confederation First Bank (CFB), monitors the default rate on personal loans among CFB members. 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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Reflective Thinking
41. Ophelia McPhee, VP of Consumer Credit, Confederation First Bank (CFB), monitors the default rate on personal loans among CFB members. 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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
42. Ophelia McPhee, VP of Consumer Credit, Confederation First Bank (CFB), monitors the default rate on personal loans among CFB members. 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
43. Ophelia McPhee, VP of Consumer Credit, Confederation First Bank (CFB), monitors the default rate on personal loans among CFB members. 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
44. The senior 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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Reflective Thinking
45. The senior 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
Difficulty: Easy
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
46. The senior 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Application
AACSB: Analytic
47. The senior 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
Difficulty: Medium
Learning Objective: Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.
Section Reference: 16.1 Chi-Square Goodness-of-Fit Test
Bloom’s: Analysis
AACSB: Reflective Thinking
48. 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
49. 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
50. 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
51. 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
52. 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Knowledge
AACSB: Reflective Thinking
53. 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) 5.992
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
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 observed chi-square value is ___.
a) 0
b) 0.69
c) 1.54
d) 21.28
e) 8.29
Difficulty: Medium
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
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 expected frequency in row 1 (A) column 1 (C) is ___.
a) 9.6
b) 12
c) 16
d) 10
e) 20
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
56. Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies 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:
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”
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Reflective Thinking
57. Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies 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:
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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
58. Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies 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:
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
Difficulty: Medium
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
59. Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies 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:
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
Difficulty: Hard
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Analysis
AACSB: Reflective Thinking
60. Catherine Lee, 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”
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Reflective Thinking
61. Catherine Lee, 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
62. Catherine Lee, 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
Difficulty: Medium
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
63. Catherine Lee, 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
Difficulty: Hard
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Analysis
AACSB: Reflective Thinking
64. Anita Gill 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
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Reflective Thinking
65. Anita Gill 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, the critical chi-square value is ___.
a) 9.21
b) 7.88
c) 15.09
d) 16.81
e) 18.81
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
66. Anita Gill 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, the critical chi-square value is ___.
a) 9.21
b) 7.88
c) 15.09
d) 5.99
e) 7.89
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
67. Anita Gill 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, the observed chi-square value is ___.
a) 24.93
b) 8.17
c) 32.89
d) 6.59
e) 4.89
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
68. Anita Gill 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, 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
Difficulty: Hard
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Analysis
AACSB: Reflective Thinking
69. A gasoline distributor wonders whether an individual’s income levels 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”
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Reflective Thinking
70. A gasoline distributor wonders whether an individual’s income levels 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, the critical chi-square value is ___.
a) 15.09
b) 7.88
c) 9.21
d) 16.81
e) 17.89
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
71. A gasoline distributor wonders whether an individual’s income levels 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, the observed chi-square value is ___.
a) 24.93
b) 4.44
c) 32.89
d) 51.79
e) 54.98
Difficulty: Medium
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
72. A gasoline distributor wonders whether an individual’s income levels 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, the critical chi-square value is ___.
a) 15.09
b) 5.99
c) 9.21
d) 16.81
e) 23.87
Difficulty: Easy
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
73. A gasoline distributor wonders whether an individual’s income levels 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, the observed chi-square value is ___.
a) 15.79
b) 4.44
c) 32.89
d) 51.79
e) 5.79
Difficulty: Medium
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Application
AACSB: Analytic
74. A gasoline distributor wonders whether an individual’s income levels 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, 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
Difficulty: Hard
Learning Objective: Use the chi-square test of independence to perform contingency analysis.
Section Reference: 16.2 Contingency Analysis: Chi-Square Test of Independence
Bloom’s: Analysis
AACSB: Reflective Thinking
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