Deck 12: Chi-Square Tests

Question 1

A goodness-of-fit test analyzes for two qualitative variables whereas a chi-square test of a contingency table is for a single qualitative variable.

Answer 1

False

Question 2

For the goodness-of-fit test,the expected category frequencies found are the:

A)sample proportions
B)hypothesized proportions
C)average of the hypothesized and sample proportions
D)proportions specified under the alternative hypothesis

Answer 2

hypothesized proportions

Question 3

Which of the following null hypotheses is used to test if five population proportions are the same?

A)
B)
C)
D)

Answer 3

Question 4

For a chi-square test of a contingency table,the expected frequencies for each cell are calculated assuming the null hypothesis is true.

Question 5

The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.

Question 6

For the goodness-of-fit test,the chi-square test statistic will:

A)always equal zero
B)always be negative
C)be at least zero
D)always be equal to n

Question 7

For a chi-square test of a contingency table,the degrees of freedom are calculated as (r - 1)(c - 1)where r and c are the number of rows and columns in the contingency table.

Question 8

The chi-square test of a contingency table is a test of independence for:

A)A single qualitative variable
B)Two qualitative variables
C)Two quantitative variables
D)Three or more quantitative variables

Question 9

For a chi-square goodness-of-fit test,the expected category frequencies are calculated using the sample category proportions.

Question 10

For a multinomial experiment,which of the following is not true?

A)The number of categories is at least two,
B)The trials are dependent
C)The sum of the category probabilities is 1,
D)The category probabilities are the same for each trial

Question 11

For the goodness-of-fit test,the sum of the expected frequencies must equal:

A)
B)n
C)k
D)k - 1

Question 12

If the null hypothesis is rejected by the goodness-of-fit test,the alternative hypothesis specifies which of the population proportions differ from their hypothesized values.

Question 13

The chi-square test of a contingency table is valid when the expected cell frequencies are:

A)Equal to 0
B)More than 0 but less than 5
C)At least 5
D)Negative

Question 14

When applying the goodness-of-fit test for normality,the quantitative data must be converted into a qualitative format.

Question 15

For a multinomial experiment with k categories,the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.

Question 16

For a chi-square test of a contingency table,each observation may be counted in multiple cells of the contingency table.

Question 17

For the Jarque-Bera test for normality,the test statistic is assumed to have a chi-square distribution with 2 degrees of freedom.

Question 18

For the chi-square test of a contingency table,the expected cell frequencies are found as which is the same as:

A)The observed cell frequencies
B)The cell probability multiplied by the sample size
C)The row total
D)The column total

Question 19

What are the degrees of freedom for the goodness-of-fit test for normality?

A)2
B)k - 3
C)k - 2
D)k - 1

Question 20

For the chi-square test of a contingency table,the expected cell frequencies are found as:

A)The row total multiplied by the column total divided by the sample size
B)The observed cell frequency
C)(r - 1)(c - 1)
D)(r)(c)

Question 21

If a test statistic has a value of X and is assumed to be χ² distributed with df degrees of freedom,then the p-value for a right-tailed test found by Excel is:

A)CHISQ.DIST.RT(X,df)
B)CHISQ.DIST.RT(df,X)
C)1-CHISQ.DIST.RT(X,df)
D)1-CHISQ.DIST.RT(df,X)

Question 22

Suppose you want to determine if mutual funds quarterly returns have a normal distribution using quantitative summary statistics.The most appropriate test is the:

A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Question 23

Suppose you want to determine if gender and major are independent.Which test should you use?

A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Question 24

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.For the goodness-of-fit test,the value of the test statistic is:

A)2.25
B)3.125
C)6.45
D)7.815

Question 25

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.Using the p-value approach and α = 0.05,the decision and conclusion are:

A)Do not reject the null hypothesis,all of the population proportions are the same
B)Reject the null hypothesis,conclude that not all proportions are equal to 0.20
C)Reject the null hypothesis,conclude that not all proportions are equal to 0.25
D)Do not reject the null hypothesis,cannot conclude that not all of the proportions are equal to 0.25

Question 26

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.For the goodness-of-fit test,the alternative hypothesis states that

A)
B)
C)
D)

Question 27

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 28

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.For the goodness-of-fit test,the degrees of freedom are:

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

Question 29

For the goodness-of-fit test for normality to be applied,what is the minimum number of qualitative intervals the quantitative data can be converted to?

A)2
B)4
C)5
D)10

Question 30

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.For the goodness-of-fit test,the assumed degrees of freedom are:

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

Question 31

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.To test if the poker dealing machine deals cards at random,the null and alternative hypotheses are:

A)
B)
C)
D)

Question 32

Suppose you want to determine if mutual funds quarterly returns have a normal distribution when your available data is partitioned into some non-overlapping intervals with given frequencies.The most appropriate test is the:

A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Question 33

For the goodness-of-fit test for normality,the null and alternative hypotheses are:

A)
B)
C)
D)

Question 34

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.At the 5% significance level,the critical value is:

A)6.251
B)7.815
C)9.348
D)11.345

Question 35

The calculation of the Jarque-Bera test statistic involves:

A)Only the sample size
B)The sample size,standard deviation,and average
C)The sample size,skewness coefficient,and the kurtosis coefficient
D)The sample average,skewness coefficient,and the kurtosis coefficient

Question 36

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.What is the value of the goodness-of-fit test statistic?

A)3.08
B)15.09
C)15.64
D)16.75

Question 37

For the Jarque-Bera test for normality,the null and alternative hypotheses are:

A)
B)
C)
D)

Question 38

Packaged candies have three different types of colors,suppose you want to determine if the population proportion of each color is the same.The most appropriate test is the:

A)Goodness-of-fit test for a multinomial experiment
B)Chi-square test for independence
C)Goodness-of-fit test for normality
D)Jarque-Bera test for normality

Question 39

For the chi-square test for normality,the expected frequencies for each interval must be:

A)Exactly 2
B)k - 3
C)At least 5
D)k - 1

Question 40

Exhibit 12-1 A card dealing machine deals spades (1),hearts (2),clubs (3),and diamonds (4)at random as if from an infinite deck.In a randomness check,1,600 cards were dealt and counted.The results are shown below. Refer to Exhibit 12.1.Using the critical value approach,the decision and conclusion are:

A)Do not reject the null hypothesis,cannot conclude that not all of the proportions are equal to 0.25
B)Do not reject the null hypothesis,all of the population proportions are the same
C)Reject the null hypothesis,conclude that not all proportions are equal to 0.25
D)Reject the null hypothesis,conclude that not all proportions are equal to 0.20

Question 41

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.Using the p-value approach and α = 0.01,the decision and conclusion are:

A)Do not reject the null hypothesis;all proportions are equal to
B)Do not reject the null hypothesis;cannot conclude that not all of the proportions are the same
C)Reject the null hypothesis;at least one of the proportions is different from its hypothesized value
D)Reject the null hypothesis;all of the proportions are not the same

Question 42

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.Using the critical value approach,the decision and conclusion are:

A)Reject the null hypothesis,not all of the proportions are the same
B)Reject the null hypothesis,all of the proportions are not the same
C)Do not reject the null hypothesis,all of the proportions are the same
D)Do not reject the null hypothesis,cannot conclude not all of the proportions are the same

Question 43

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.At the 10% significance level,the critical value is:

A)6.635
B)5.024
C)3.841
D)2.706

Question 44

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.For the goodness-of -fit test,the null and alternative hypotheses are:

A)
B)
C)
D)

Question 45

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.Using the p-value approach and α = 0.10,the decision and conclusion are:

A)Reject the null hypothesis,gender and candidate preference are dependent
B)Do not reject the null hypothesis,gender and candidate preference are independent
C)Reject the null hypothesis,gender and candidate preference are independent
D)Do not reject null hypothesis,gender and candidate preference are dependent

Question 46

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.For the chi-square test of independence,the assumed degrees of freedom are:

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

Question 47

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.Which of the following is the expected joint probability for the 'low income and 21-35 age group' cell assuming age group and income are independent?

A)0.0830
B)0.0874
C)0.0996
D)0.1328

Question 48

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.Using the critical value approach,the decision and conclusion are:

A)Reject the null hypothesis,gender and candidate preference are dependent
B)Do not reject the null hypothesis,gender and candidate preference are independent
C)Reject the null hypothesis,gender and candidate preference are independent
D)Do not reject the null hypothesis,gender and candidate preference are dependent

Question 49

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.To test that gender and candidate preference are independent,the null and alternative hypothesis are:

A)
B)
C)
D)

Question 50

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 51

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.Which of the following is the estimated joint probability for the 'low income and 21-35 age group' cell?

A)0.0830
B)0.0874
C)0.0996
D)0.1328

Question 52

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.What is the value of goodness-of-fit chi-square test statistic?

A)0.605
B)0.632
C)1.62
D)2.57

Question 53

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.Using the p-value approach and α = 0.05,the decision and conclusion are:

A)Do not reject the null hypothesis,all of the proportions are the same
B)Do not reject the null hypothesis,cannot conclude that not all of the proportions are the same
C)Reject the null hypothesis,not all of the proportions are the same
D)Reject the null hypothesis,all of the proportions are not the same

Question 54

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.For the goodness-of-fit test,what are the degrees of freedom for the chi-squared test statistic?

A)4
B)5
C)6
D)7

Question 55

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 56

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.At the 1% significance level,the critical value is:

A)9.236
B)11.070
C)12.833
D)15.086

Question 57

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.For the chi-square test of independence,the value of the test statistic is:

A)2.34
B)1.62
C)3.25
D)4

Question 58

Exhibit 12.3 A fund manager wants to know if it equally likely that the Dow Jones Industrial average will go up each day of the week.For each day of the week,the fund manager observes the following number of days when the Dow Jones Industrial average goes up. Refer to Exhibit 12.3.At the 5% significance level,the critical value is:

A)7.779
B)9.488
C)11.143
D)13.277

Question 59

Exhibit 12.2 A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to insure each college is represented fairly.The below table shows the observed number students that participate in the poll from each college and the actual proportion of students in each college. Refer to Exhibit 12.2.Using the critical value approach,the decision and conclusion are:

A)Reject the null hypothesis,at least one of the proportions is different from its hypothesized value
B)Reject the null hypothesis,all of the proportions are not the same
C)Do not reject the null hypothesis,all proportions are equal to 0.20
D)Do not reject the null hypothesis,cannot conclude not all of the proportions are the same

Question 60

Exhibit 12.4 In the following table,likely voters' preferences of two candidates are cross-classified by gender. Refer to Exhibit 12.4.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 61

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.Using the critical value approach,the decision and conclusion are:

A)Do not reject the null hypothesis,age and income are dependent
B)Do not reject the null hypothesis,age and income are independent
C)Reject the null hypothesis,age and income are dependent
D)Reject the null hypothesis,age and income are independent

Question 62

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.For the chi-square test of independence,the value of the test statistic is:

A)12.221
B)15.378
C)17.853
D)20.154

Question 63

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.To test that age group and income are independent,the null and alternative hypothesis are:

A)
B)
C)
D)

Question 64

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.For the chi-square test of independence,the value of the test statistic is:

A)8.779
B)10.840
C)13.243
D)16.159

Question 65

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.The row total for Asians is:

A)86
B)75
C)62
D)31

Question 66

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.Assuming that race and seniority are independent,what is the expected frequency of Asian directors?

A)0
B)1.95
C)3.91
D)5.42

Question 67

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.The column total for directors is:

A)16
B)56
C)73
D)109

Question 68

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 69

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.Using the p-value approach and α = 0.05,the decision and conclusion are:

A)Do not reject the null hypothesis,age and income are dependent
B)Do not reject the null hypothesis,age and income are independent
C)Reject the null hypothesis,age and income are dependent
D)Reject the null hypothesis,age and income are independent

Question 70

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.At the 5% significance level,the critical value is:

A)14.684
B)16.919
C)19.023
D)21.666

Question 71

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.For the chi-square test of independence,the degrees of freedom are:

A)2
B)4
C)9
D)8

Question 72

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.Using the critical value approach,the decision and conclusion are:

A)Reject the hypothesis,conclude race and seniority are dependent
B)Reject the null hypothesis,conclude race and seniority are independent
C)Do not reject the null hypothesis,conclude race and seniority are dependent
D)Do not reject the null hypothesis,conclude race and seniority are independent

Question 73

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.At the 5% significance level,the critical value is:

A)13.277
B)11.143
C)9.488
D)7.779

Question 74

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.The p-value is:

A)Less than 0.01
B)Between 0.01 and 0.05
C)Between 0.05 and 0.10
D)Greater than 0.10

Question 75

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.For the chi-square test for independence,the degrees of freedom used are:

A)2
B)16
C)9
D)0

Question 76

Exhibit 12.5 In the following table,individuals are cross-classified by their age group and income level. Refer to Exhibit 12.5.Assuming age group and income are independent,the expected 'low income and 21-35 age group' cell frequency is:

A)105.27
B)107.72
C)146.31
D)178.42

Question 77

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.6.To test that race and seniority are independent,the null and alternative hypothesis are:

A)
B)
C)
D)

Question 78

Exhibit 12.7 The heights (in cm)for a random sample of 60 males were measured.The sample mean is 166.55,the standard deviation is 12.57,the sample kurtosis is 0.12,and the sample skewness is -0.23.The following table shows the heights subdivided into non-overlapping intervals. Refer to Exhibit 12.7.The heights are subdivided into five intervals.The degrees of freedom for the goodness-of-fit test for normality is:

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

Question 79

Exhibit 12.6 The following table shows the distribution of employees in an Organization.Martha Foreman,an analyst wants to see if race has a bearing on the position a person holds with this company. Refer to Exhibit 12.5.Using the p-value approach and α = 0.05,the decision and conclusion are:

A)Reject the null hypothesis,conclude race and seniority are dependent
B)Reject the null hypothesis,conclude race and seniority are independent
C)Do not reject the null hypothesis,cannot conclude race and seniority are dependent
D)Do not reject the null hypothesis,conclude race and seniority are independent

Question 80

Exhibit 12.7 The heights (in cm)for a random sample of 60 males were measured.The sample mean is 166.55,the standard deviation is 12.57,the sample kurtosis is 0.12,and the sample skewness is -0.23.The following table shows the heights subdivided into non-overlapping intervals. Refer to Exhibit 12.7.For the chi-square test for normality,the null and alternative hypothesis are:

A)
B)
C)
D)