Deck 16: Analysis of Categorical Data

Question 1

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.

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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.

Question 5

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.

Question 6

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.

Question 7

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

Question 8

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

Question 9

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

Question 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.

Question 11

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 $\alpha$ = .01, the observed value of chi-square is ___.

A)12.09
B)9.82
C)13.28
D)17.81
E)2.09

Question 12

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 $\alpha$ = .01, the critical value of chi-square is ___.

A)7.78
B)15.09
C)9.24
D)13.28
E)15.48

Question 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.

Question 14

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

Question 15

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

Question 16

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.

Question 17

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 $\alpha$ = .01, the degrees of freedom for this test are ___.

A)5
B)4
C)3
D)2
E)1

Question 18

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.

Question 19

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

Question 20

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

Question 21

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

Question 22

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. Using $\alpha$ = 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

Question 23

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

Question 24

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: Using $\alpha$ = 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

Question 25

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Using $\alpha$ = 0.10, the critical value of chi-square for the data is ___.

A)9.236
B)7.779
C)1.064
D)13.277
E)12.89

Question 26

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

Question 27

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 $\alpha$ = .01, the critical chi-square value is ___.

A)13.278
B)15.086
C)7.779
D)11.070
E)14.356

Question 28

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

A)5
B)4
C)3
D)2
E)1

Question 29

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 $\alpha$ = .01, the observed chi-square value is ___.

A)1.18
B)9.10
C)20.27
D)4.51
E)19.70

Question 30

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 $\alpha$ = .05, the critical chi-square value is ___.

A)13.277
B)15.086
C)7.8147
D)11.070
E)15.546

Question 31

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 $\alpha$ = .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

Question 32

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

Question 33

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 $\alpha$ = .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

Question 34

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 $\alpha$ = .05, the observed chi-square value is ___.

A)5.418
B)9.10
C)20.27
D)4.51
E)7.86

Question 35

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 $\alpha$ = .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

Question 36

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 $\alpha$ = .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

Question 37

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) $\mu$$\le$ 30
D) $\mu$ > 30
E)s > 30

Question 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: 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

Question 39

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

Question 40

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 $\alpha$ = .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

Question 41

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 $\alpha$ = 0.05, the critical value of chi-square is ___.

A)7.38
B)5.02
C)3.84
D)5.99
E)6.99

Question 42

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: 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"

Question 43

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

Question 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 $\alpha$ = 0.05, the null hypothesis is ___.

A) $\mu$ > 80
B) $\mu$$\le$ 80
C)p > 0.50
D)p = 0.50
E)s ≥ 0.80

Question 45

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 $\alpha$ = 0.01, critical chi-square value is ___.

A)6.63
B)9.21
C)7.88
D)10.60
E)12.34

Question 46

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: 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"

Question 47

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: The observed value of chi-square is ___.

A)5.99
B)28.30
C)32.35
D)60.65
E)50.78

Question 48

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

Question 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

Question 50

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'. Using $\alpha$ = 0.05, the expected frequency in row 1 (A)column 1 (C)is ___.

A)9.6
B)12
C)16
D)10
E)20

Question 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

Question 52

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 $\alpha$ = 0.05, the observed value of chi-square is ___.

A)8.00
B)2.82
C)4.00
D)9.71
E)9.97

Question 53

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

Question 54

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: Using $\alpha$ = .05, the critical value of chi-square is ___.

A)5.99
B)3.84
C)5.02
D)7.37
E)9.99

Question 55

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 $\alpha$ = 0.01, observed chi-square value is ___.

A)13.38
B)26.29
C)2.09
D)1.05
E)3.98

Question 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: Using $\alpha$ = .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

Question 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'. Using $\alpha$ = 0.05, the critical chi-square value is ___.

A)9.488
B)1.386
C)8.991
D)3.357
E)5.992

Question 58

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 $\alpha$ = 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 $\mu$ > 30
D)do not reject the null hypothesis $\mu$$\le$ 30
E)do nothing

Question 59

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 $\alpha$ = 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 $\mu$ > 80
D)do not reject the null hypothesis $\mu$$\le$ 80
E)do nothing

Question 60

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'. Using $\alpha$ = 0.05, the observed chi-square value is ___.

A)0
B)0.69
C)1.54
D)21.28
E)8.29

Question 61

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .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

Question 62

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. 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"

Question 63

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: 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

Question 64

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .05, the critical chi-square value is ___.

A)15.09
B)5.99
C)9.21
D)16.81
E)23.87

Question 65

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: Using $\alpha$ = .05, the critical value of chi-square is ___.

A)5.02
B)3.84
C)7.37
D)6.09
E)5.99

Question 66

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: Using $\alpha$ = .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

Question 67

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .01, the observed chi-square value is ___.

A)24.93
B)4.44
C)32.89
D)51.79
E)54.98

Question 68

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .01, the critical chi-square value is ___.

A)15.09
B)7.88
C)9.21
D)16.81
E)17.89

Question 69

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: Using $\alpha$ = .01, the critical chi-square value is ___.

A)9.21
B)7.88
C)15.09
D)16.81
E)18.81

Question 70

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: Using $\alpha$ = .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

Question 71

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: Using $\alpha$ = .05, the critical chi-square value is ___.

A)9.21
B)7.88
C)15.09
D)5.99
E)7.89

Question 72

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: Using $\alpha$ = .05, the observed value of chi-square is ___.

A)5.28
B)9.49
C)13.19
D)16.79
E)18.79

Question 73

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: Using $\alpha$ = .01, the observed chi-square value is ___.

A)24.93
B)8.17
C)32.89
D)6.59
E)4.89

Question 74

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .05, the observed chi-square value is ___.

A)15.79
B)4.44
C)32.89
D)51.79
E)5.79