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Chi-Square Analysis True/False & Multiple Choice
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File: Ch16, Chapter 16: Chi-Square Analysis

True/False

1. In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

2. In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

3. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

4. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

5. A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a normal distribution (the mean and the standard deviation of which must be estimated) for a data with "k" categories. This test has (k-3) degrees of freedom.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

6. The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

7. The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

8. When using the chi-square goodness-of-fit test, we must make sure that none of the expected frequencies is less than 30.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

9. A chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

10. A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

11. A two-way table used for a test of independence is sometimes called a contingency table.

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

12. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 12.

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

13. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 7.

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

14. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 6.

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

15. The null hypothesis for a chi-square test of independence is that the two variables are not related.

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

Multiple Choice

16.          A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C) more than the other two.  A sample of 60 consumers is used.  What is the expected frequency for category A?

a) 1/3

b) 20

c) 60

d) 10

e) 30

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

17.          A goodness of fit test is to be performed to see if Web Surfers prefer any of four Web sites (A, B, C and D) more than the other three.  A sample of 60 consumers is used.  What is the expected frequency for Web site A?

a) 1/4

b) 20

c) 15

d) 10

e) 30

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

18.          A variable contains five categories.  It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.  Using  = .01, the degrees of freedom for this test are _______.

a) 5

b) 4

c) 3

d) 2

e) 1

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

19.          A variable contains five categories.  It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.  Using  = .01, the critical value of chi-square is _______.

a) 7.78

b) 15.09

c) 9.24

d) 13.28

e) 15.48

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

20.          A variable contains five categories.  It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.  Using  = .01, the observed value of chi-square is _______.

a) 12.09

b) 9.82

c) 13.28

d) 17.81

e) 2.09

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Middle

21.          A variable contains five categories.  It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.  Using  = .01, the appropriate decision is _______.

a) reject the null hypothesis that the observed distribution is uniform

b) reject the null hypothesis that the observed distribution is not uniform

c) do not reject the null hypothesis that the observed distribution is uniform

d) do not reject the null hypothesis that the observed distribution is not uniform

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

22.          A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26.  Using  = .01, the critical chi-square value is _______.

a) 13.277

b) 15.086

c) 7.779

d) 11.070

e) 14.356

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

23.          A variable contains five categories. It is expected that data are uniformly distributed across these five categories.  To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26.  Using  = .01, the observed chi-square value is _______.

a) 1.18

b) 9.10

c) 20.27

d) 4.51

e) 19.70

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

24.          A variable contains five categories. It is expected that data are uniformly distributed across these five categories.  To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26.  Using  = .01, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

b) do not reject the null hypothesis that the observed distribution is not uniform

c) reject the null hypothesis that the observed distribution is uniform

d) reject the null hypothesis that the observed distribution is not uniform

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

25.          A variable contains five categories. It is expected that data are uniformly distributed across these five categories.  To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26.  Using  = .10, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

b) do not reject the null hypothesis that the observed distribution is not uniform

c) reject the null hypothesis that the observed distribution is uniform

d) reject the null hypothesis that the observed distribution is not uniform

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

26.          A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.  Using  = .05, the critical chi square value is _______.

a) 13.277

b) 15.086

c) 7.8147

d) 11.070

e) 15.546

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

27.          A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.  Using  = .05, the observed chi-square value is _______.

a) 5.418

b) 9.10

c) 20.27

d) 4.51

e) 7.86

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

28.          A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.  Using  = .05, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

b) do not reject the null hypothesis that the observed distribution is not uniform

c) reject the null hypothesis that the observed distribution is uniform

d) reject the null hypothesis that the observed distribution is not uniform

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

29.          A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.  Using  = .10, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

b) do not reject the null hypothesis that the observed distribution is not uniform

c) reject the null hypothesis that the observed distribution is uniform

d) reject the null hypothesis that the observed distribution is not uniform

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

30.          A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.  There are 6 categories, and lambda must be estimated.  How many degrees of freedom should be used?

a) 6

b) 5

c) 4

d) 3

e) 2

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

31.          A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.  There are 8 categories, and lambda must be estimated.  How many degrees of freedom should be used?

a) 8

b) 7

c) 6

d) 5

e) 4

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

32.          A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. Alpha is chosen to be 0.10.  The critical (table) value of chi-square is _______.

a) 10.645

b) 12.017

c) 3.828

d) 16.812

e) 17.345

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

33.          A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

Category              0              1              2              3              4              5

Observed            47           56           39           22           18           10

Using  = 0.10, the critical chi-square value for this goodness-of-fit test is _______.

a) 1.064

b) 13.277

c) 9.236

d) 8.799

e) 7.779

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

34.          A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

Category              0              1              2              3              4              5

Observed            47           56           39           22           18           10

Using  = 0.10, the observed chi-square value for this goodness-of-fit test is ____.

a) 2.28

b) 14.56

c) 17.43

d) 1.68

e) 2.67

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

35. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

Category              0              1              2              3              4              >5

Observed            7              18           25           17           12           5

Using  = 0.10, the critical value of chi-square for the data is _______.

a) 9.236

b) 7.779

b) 1.064

c) 13.277

d) 12.89

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

36.          A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

Category              0              1              2              3              4              >5

Observed            7              18           25           17           12           5

Using  = 0.10, the value of the observed chi-square for the data is _______.

a) 19.37

b) 2.29

c) 1.74

d) 3.28

e) 4.48

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

37.          Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.  He collected a random sample and constructed the following frequency distribution to test his hypothesis.

Cars per 15 minute interval          0              1              2              3              4              >5

Observed Frequency     5              15           17           12           10           8

The number of degrees of freedom for this goodness-of-fit test is _______.

a) 5

b) 4

c) 3

d) 2

e) 1

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

38.          Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.  He collected a random sample and constructed the following frequency distribution to test his hypothesis.

Cars per 15 minute interval          0              1              2              3              4              >5

Observed Frequency     5              15           17           12           10           8

Using  = 0.05, the critical value of chi-square for this goodness-of-fit test is ____.

a) 9.49

b) 7.81

c) 7.78

d) 11.07

e) 12.77

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

39.          Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.  He collected a random sample and constructed the following frequency distribution to test his hypothesis.

Cars per 15 minute interval          0              1              2              3              4              >5

Observed Frequency     5              15           17           12           10           8

The observed value of chi-square for this goodness-of-fit test is _____.

a) 0.73

b) 6.72

c) 3.15

d) 7.81

e) 9.87

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

40.          Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.  He collected a random sample and constructed the following frequency distribution to test his hypothesis.

Cars per 15 minute interval          0              1              2              3              4              >5

Observed Frequency     5              15           17           12           10           8

Using  = 0.05, the appropriate decision for this goodness-of-fit test is ____.

a) reject the null hypothesis that the observed distribution is Poisson

b) reject the null hypothesis that the observed distribution is not Poisson

c) do not reject the null hypothesis that the observed distribution is not Poisson

d) do not reject the null hypothesis that the observed distribution is Poisson

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

41.          Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks.  One of her standards is: "no more than 5% of personal loans should be in default."  On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.

a) p > 0.05

b) p = 0.05

c)   30

d)  > 30

e) s > 30

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

42.          Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks.  One of her standards is "no more than 5% of personal loans should be in default."  On each Friday, the default rate is calculated for a sample of 500 personal loans.  Last Friday's sample contained 30 defaulted loans.  Using  = 0.01, critical chi-square value is _______.

a) 6.63

b) 9.21

c) 7.88

d) 10.60

e) 12.34

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

43.          Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks.  One of her standards is "no more than 5% of personal loans should be in default."  On each Friday, the default rate is calculated for a sample of 500 personal loans.  Last Friday's sample contained 30 defaulted loans.  Using  = 0.01, observed chi-square value is _______.

a) 13.38

b) 26.29

c) 2.09

d) 1.05

e) 3.98

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

44.          Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks.  One of her standards is "no more than 5% of personal loans should be in default."  On each Friday, the default rate is calculated for a sample of 500 personal loans.  Last Friday's sample contained 30 defaulted loans.  Using  = 0.01, the appropriate decision is _______.

a) reject the null hypothesis p > 0.05

b) do not reject the null hypothesis p = 0.05

c) reject the null hypothesis  > 30

d) do not reject the null hypothesis   30

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

45.          The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree."  A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian.  Using  = 0.05, the null hypothesis is __________.

a)  > 80

b)   80

c) p > 0.50

d) p = 0.50

e) s ≥ 0.80

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

46.          The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree."  A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian.  Using  = 0.05, the critical value of chi-square is _______.

a) 7.38

b) 5.02

c) 3.84

d) 5.99

e) 6.99

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

47.          The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree."  A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian.  Using  = 0.05, the observed value of chi-square is __________.

a) 8.00

b) 2.82

c) 4.00

d) 9.71

e) 9.97

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

48.          The executives of CareFree Insurance, Inc. feel that "a minority of our employees perceive an authoritarian management style at CareFree."  A random sample of 200 CareFree employees is selected to test this hypothesis. Eighty employees rate the management as authoritarian.  Using  = 0.05, the appropriate decision is ________.

a) do not reject the null hypothesis p > 0.50

b) reject the null hypothesis p = 0.50

c) reject the null hypothesis  > 80

d) do not reject the null hypothesis   80

e) do nothing

Ans:

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

49.          A test of independence is to be performed. The contingency table has 4 rows and 5 columns. What would the degrees of freedom be?

a) 20

b) 9

c) 7

d) 12

e) 19

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

50.          A contingency table is to be used to test for independence.  There are 3 rows and 3 columns in the table.  How many degrees of freedom are there for this problem?

a) 6

b) 5

c) 4

d) 3

e) 1

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

51.          A contingency table has five rows and six columns.  When applying a chi-square test of independence to this table, the number of degrees of freedom is _____.

a) 9

b) 20

c) 30

d) 11

e) 12

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

52.          A contingency table has seven rows and five columns.  When applying a chi-square test of independence to this table, the number of degrees of freedom is _____.

a) 24

b) 35

c) 12

d) 10

e) 11

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

53.          Contingency tables should not be used with expected cell frequencies _______.

a) less than the number of rows

b) less than the number of columns

c) less than 5

d) less than 30

e) less than 50

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

54.          Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'.

C             D             E

A             12           10           8

B             20           24           26

Using  = 0.05, the critical chi-square value is _______.

a) 9.488

b) 1.386

c) 8.991

d) 3.357

e) 5.991

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

55.          Use the following set of observed frequencies to test the independence of the two variables.  Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'.

C             D             E

A             12           10           8

B             20           24           26

Using  = 0.05, the observed chi-square value is _______.

a) 0

b) 0.69

c) 1.54

d) 21.28

e) 8.29

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

56.          Use the following set of observed frequencies to test the independence of the two variables.  Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'.

C             D             E

A             12           10           8

B             20           24           26

Using  = 0.05, the expected frequency in row 1 (A) column 1 (C) is _______.

a) 9.6

b) 12

c) 16

d) 10

e) 20

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

57.          Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine.  He wonders whether subscriptions are influenced by the head of household’s employment classification.  His staff prepared the following contingency table from a random sample of 300 households.

Clerical  Managerial         Professional

Subscribes          Yes         10           90           60

No          60           60           20

Sam's null hypothesis is ______________.

a) "head of household classification" is related to "subscribes"

b) "head of household classification" is not independent of "subscribes"

c) "head of household classification" is independent of "subscribes”

d) "head of household classification" influences "subscribes"

e)  “clerical is not related to managerial”

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

58.          Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine.  He wonders whether subscriptions are influenced by the head of household’s employment classification.  His staff prepared the following contingency table from a random sample of 300 households.

Clerical  Managerial         Professional

Subscribes          Yes         10           90           60

No          60           60           20

Using  = .05, the critical value of chi-square is ______________.

a) 5.99

b) 3.84

c) 5.02

d) 7.37

e) 9.99

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

59.          Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine.  He wonders whether subscriptions are influenced by the head of household’s employment classification.  His staff prepared the following contingency table from a random sample of 300 households.

Clerical  Managerial         Professional

Subscribes          Yes         10           90           60

No          60           60           20

The observed value of chi-square is ______________.

a) 5.99

b) 28.30

c) 32.35

d) 60.65

e) 50.78

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

60.          Sam Hill, Director of Media Research, is analyzing subscribers to the Life West of the Saline magazine.  He wonders whether subscriptions are influenced by the head of household’s employment classification.  His staff prepared the following contingency table from a random sample of 300 households.

Clerical  Managerial         Professional

Subscribes          Yes         10           90           60

No          60           60           20

Using  = .05, the appropriate decision is ______________.

a) reject the null hypothesis and conclude the two variables are independent

b) do not reject the null hypothesis and conclude the two variables are independent

c) reject the null hypothesis and conclude the two variables are not independent

d) do not reject the null hypothesis and conclude the two variables are not independent

e) do nothing

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: High

61.          Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.  She wonders whether acceptance is influenced by children in the household.  Her staff prepared the following contingency table from a random sample of 100 households.

Children in Household

Pre-teenagers   teenagers           none

Preferred Package          Pump    30           20           10

Tube      10           10           20

Catherine's null hypothesis is ______________.

a) "children in household" is not independent of "preferred package"

b) "children in household" is independent of "preferred package"

c) "children in household" is related to "preferred package"

d) "children in household" influences "preferred package"

e) “pump” is independent of “tube”

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

62.          Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.  She wonders whether acceptance is influenced by children in the household.  Her staff prepared the following contingency table from a random sample of 100 households.

Children in Household

Pre-teenagers   teenagers           none

Preferred Package          Pump    30           20           10

Tube      10           10           20

Using  = .05, the critical value of chi-square is ______________.

a) 5.02

b) 3.84

c) 7.37

d) 6.09

e) 5.99

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

63.          Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.  She wonders whether acceptance is influenced by children in the household.  Her staff prepared the following contingency table from a random sample of 100 households.

Children in Household

Pre-teenagers   teenagers           none

Preferred Package          Pump    30           20           10

Tube      10           10           20

Using  = .05, the observed value of chi-square is ______________.

a) 5.28

b) 9.49

c) 13.19

d) 16.79

e) 18.79

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

64.          Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.  She wonders whether acceptance is influenced by children in the household.  Her staff prepared the following contingency table from a random sample of 100 households.

Children in Household

Pre-teenagers   teenagers           none

Preferred Package          Pump    30           20           10

Tube      10           10           20

Using  = .05, the appropriate decision is ______________.

a) reject the null hypothesis and conclude the two variables are not independent

b) do not reject the null hypothesis and conclude the two variables are not independent

c) reject the null hypothesis and conclude the two variables are independent

d) do not reject the null hypothesis and conclude the two variables are independent

e) do nothing

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Hard

65.          Anita Cruz recently assumed responsibility for a large investment portfolio.  She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks.

Investment        Industry Sector

Objective            Electronics          Airlines Healthcare

Growth                100         10           40

Income 20           20           10

Anita's null hypothesis is ______________.

a) "investment objective" is related to "industry sector"

b) "investment objective" influences "industry sector"

c) "investment objective" is not independent of "industry sector"

d) "investment objective" is independent of "industry sector"

e) “growth” and “income” are independent

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

66.          Anita Cruz recently assumed responsibility for a large investment portfolio.  She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks.

Investment        Industry Sector

Objective            Electronics          Airlines Healthcare

Growth                100         10           40

Income 20           20           10

Using  = .01, critical chi-square value is ______________.

a) 9.21

b) 7.88

c) 15.09

d) 16.81

e) 18.81

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

67.          Anita Cruz recently assumed responsibility for a large investment portfolio.  She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks.

Investment        Industry Sector

Objective            Electronics          Airlines Healthcare

Growth                100         10           40

Income 20           20           10

Using  = .05, critical chi-square value is ______________.

a) 9.21

b) 7.88

c) 15.09

d) 5.99

e) 7.89

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

68.          Anita Cruz recently assumed responsibility for a large investment portfolio.  She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks.

Investment        Industry Sector

Objective            Electronics          Airlines Healthcare

Growth                100         10           40

Income 20           20           10

Using  = .01, observed chi-square value is ______________.

a) 24.93

b) 8.17

c) 32.89

d) 6.59

e) 4.89

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

69.          Anita Cruz recently assumed responsibility for a large investment portfolio.  She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks.

Investment        Industry Sector

Objective            Electronics          Airlines Healthcare

Growth                100         10           40

Income 20           20           10

Using  = .01, appropriate decision is ______________.

a) reject the null hypothesis and conclude the two variables are not independent

b) reject the null hypothesis and conclude the two variables are independent

c) do not reject the null hypothesis and conclude the two variables are not independent

d) do not reject the null hypothesis and conclude the two variables are independent

e) do nothing

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Hard

70.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             90           10           20

\$30,000 or More               60           60           60

The null hypothesis is ______________.

a) "income” is independent of "type of gasoline”

b) "income” influences "type of gasoline”

c) "income” is not independent of "type of gasoline”

d) “income" is related to "type of gasoline"

e) “regular” is independent of “premium”

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

71.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             90           10           20

\$30,000 or More               60           60           60

Using  = .01, critical chi-square value is ______________.

a) 15.09

b) 7.88

c) 9.21

d) 16.81

e) 17.89

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

72.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             90           10           20

\$30,000 or More               60           60           60

Using  = .01, observed chi-square value is ______________.

a) 24.93

b) 4.44

c) 32.89

d) 51.79

e) 54.98

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

73.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             80           30           30

\$30,000 or More               70           40           50

Using  = .05, critical chi-square value is ______________.

a) 15.09

b) 5.99

c) 9.21

d) 16.81

e) 23.87

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

74.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             80           30           30

\$30,000 or More               70           40           50

Using  = .05, observed chi-square value is ______________.

a) 15.79

b) 4.44

c) 32.89

d) 51.79

e) 5.79

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

75.          A gasoline distributor wonders whether an individual’s income level influences the grade of gasoline purchased.

Personal              Type of Gasoline

Less than \$30,000             80           30           30

\$30,000 or More               70           40           50

Using  = .05, appropriate decision is ______________.

a) reject the null hypothesis and conclude the two variables are not independent

b) reject the null hypothesis and conclude the two variables are independent

c) do not reject the null hypothesis and conclude the two variables are not independent

d) do not reject the null hypothesis and conclude the two variables are independent

e) do nothing

Ans:

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: High

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