Deck 12: Chi-Square Tests

Question 1

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

Answer 1

B

Question 2

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

Answer 2

True

Question 3

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) rc

Answer 3

A

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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 9

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

Question 10

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.

Question 11

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 12

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 13

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

A) H₀:p₁ = p₂ = p₃ = p₄ = p₅ = 0.25
B) H₀:p₁ = p₂ = p₃ = p₄ = 0.25
C) H₀:p₁ = p₂ = p₃ = p₄ = 0.20
D) H₀:p₁ = p₂ = p₃ = p₄ = p₅ = 0.20

Question 14

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 15

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

A) The number of categories is at least two,k ≥ 2.
B) The trials are dependent.
C) The sum of the cell probabilities is P₁ + P₂ + ...+ P_k = 1.
D) The category probabilities are the same for each trial.

Question 16

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 17

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 ton

Question 18

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

A) 1
B) n
C) k
D) k−1

Question 19

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

Question 20

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 21

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

A) H₀:S < 0 and K > 0,H_A:S < 0 or K < 0
B) H₀:S < 0 and K = 0,H_A:S > 0 or K ≠ 0
C) H₀:S = 0 and K = 0,H_A:S ≠ 0 or K ≠ 0
D) H₀:S = 0 and K > 0,H_A:S ≠ 0 or K < 0

Question 22

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 kurtosis coefficient
D) the sample average,skewness coefficient,and kurtosis coefficient

Question 23

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 24

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

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

Question 25

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 26

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. At the 5% significance level,the critical value is ______.

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

Question 27

Suppose you want to determine if the quarterly returns for mutual funds 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 28

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. To test if the poker-dealing machine deals cards at random,the null and alternative hypotheses are ________________________________________.

A) H₀:p₁ = p₂ = p₃ = p₄ = 0,H_A: Not all population proportions are equal to 0,25
B) H₀:p₁ = p₂ = p₃ = p₄ = 0.25,H_A: Not all population proportions are equal to 0,25
C) H₀:p₁ = p₂ = p₃ = p₄ = 1,H_A: Not all population proportions are equal to 0,25
D) H₀:p₁ = p₂ = p₃ = p₄ = 0.20,H_A: Not all population proportions are equal to 0,20

Question 29

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

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

Question 30

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. 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;we cannot conclude that not all of the proportions are equal to 0.25

Question 31

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. 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 32

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

A) H_A: Not all population proportions are equal to 0,20
B) H_A: At least one of the population proportions is different from its hypothesized value
C) H_A: Not all population proportions are the same
D) H_A: Not all population proportions are equal to 0,17

Question 33

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 34

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. 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 35

Suppose you want to determine if gender and major are independent.Which of the following tests 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 36

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. For the goodness-of-fit test,the degrees of freedom are ____.

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

Question 37

Suppose you want to determine if the quarterly returns for mutual funds 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 38

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

A) H₀: Data does not follow a normal distribution,H_A: Data follows a normal distribution
B) H₀: Data follows a normal distribution,H_A: Data does not follow a normal distribution
C) H₀: Data follows a normal distribution,H_A: Data are skewed right
D) H₀: Data follows a normal distribution,H_A: Data are skewed left

Question 39

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. Using the critical value approach,the decision and conclusion are _________________________________________.

A) do not reject the null hypothesis;we 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 40

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 using Excel's command ________________________.

A) '=CHISQ.DIST.RT(X,Deg_freedom)'
B) '=CHISQ.DIST.RT(Deg_freedom,X)'
C) '=1-CHISQ.DIST.RT(X,Deg_freedom)'
D) '=1-CHISQ.DIST.RT(Deg_freedom,X)'

Question 41

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

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

Question 42

A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to ensure each college is represented fairly.The below table shows the observed number of students who participate in the poll from each college and the actual proportion of students in each college. 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 43

A fund manager wants to know if it is 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. Which of the following is the value of goodness-of-fit chi-square test statistic?

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

Question 44

In the following table,individuals are cross-classified by their age group and income level. 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 45

In the following table,likely voters' preferences of two candidates are cross-classified by gender. To test that gender and candidate preference are independent,the null hypothesis is ___________________________.

A) H₀: Gender and candidate preference are independent
B) H₀: Gender and candidate preference are mutually exclusive
C) H₀: Gender and candidate preference are not mutually exclusive
D) H₀: Gender and candidate preference are dependent

Question 46

A fund manager wants to know if it is 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. For the goodness-of-fit test,the null and alternative hypotheses are ________________________________________.

A) H₀:p₁ = p₂ = p₃ = p₄ = 1/4,H_A: Not all population proportions are equal to 1/4
B) H₀:p₁ = p₂ = p₃ = p₄ = p₅ = 1/5,H_A: Not all population proportions are equal to 1/5
C) H₀:p₁ = p₂ = p₃ = p₄ = p₅ = 1/4,H_A: Not all population proportions are equal to 1/4
D) H₀:p₁ = p₂ = p₃ = p₄ = 1/5,H_A: Not all population proportions are equal to 1/5

Question 47

A fund manager wants to know if it is 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. 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;we cannot conclude that not all of the proportions are the same

Question 48

A fund manager wants to know if it is 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. 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;we 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 49

A fund manager wants to know if it is 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. 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 50

In the following table,likely voters' preferences of two candidates are cross-classified by gender. 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 51

A fund manager wants to know if it is 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. 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 52

In the following table,likely voters' preferences of two candidates are cross-classified by gender. 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 53

In the following table,likely voters' preferences of two candidates are cross-classified by gender. 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 54

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

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

Question 55

In the following table,likely voters' preferences of two candidates are cross-classified by gender. 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

A fund manager wants to know if it is 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. At the 5% significance level,the critical value is _______.

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

Question 57

In the following table,individuals are cross-classified by their age group and income level. 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 58

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

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

Question 59

A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to ensure each college is represented fairly.The below table shows the observed number of students who participate in the poll from each college and the actual proportion of students in each college. 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 0.20
B) do not reject the null hypothesis;we 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 60

A university has six colleges and takes a poll to gauge student support for a tuition increase.The university wants to ensure each college is represented fairly.The below table shows the observed number of students that participate in the poll from each college and the actual proportion of students in each college. 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;we cannot conclude not all of the proportions are the same

Question 61

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

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

Question 62

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. 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 63

In the following table,individuals are cross-classified by their age group and income level. 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 64

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. The row total for Asians is _____.

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

Question 65

In the following table,individuals are cross-classified by their age group and income level. 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 66

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. 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 67

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. The column total for directors is _____.

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

Question 68

In the following table,individuals are cross-classified by their age group and income level. 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

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. 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 70

In the following table,individuals are cross-classified by their age group and income level. 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 71

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. To test that race and seniority are independent,the null and alternative hypothesis are _______________________________________________________________________.

A) H₀: Race and seniority are independent;H_A: Race and seniority are dependent
B) H₀: Race and seniority are mutually exclusive;H_A: Race and seniority are not mutually exclusive
C) H₀: Race and seniority are not mutually exclusive;H_A: Race and seniority are mutually exclusive
D) H₀: Race and seniority are dependent;H_A: Race and seniority are independent

Question 72

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. 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 73

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. 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 74

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. For the chi-square test for independence,the degrees of freedom used are _____.

A) 2
B) 16
C) 9
D) 8

Question 75

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

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

Question 76

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. Assuming that race and seniority are independent,which of the following is the expected frequency of Asian directors?

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

Question 77

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. For the goodness-of-fit test for normality,the null and alternative hypothesis are ______________________________________________________________________.

A) H₀: Heights follow a normal distribution with mean 166.55 and standard deviation 12.46,H_A: Heights do not follow a normal distribution with mean 166.55 and standard deviation 12.46
B) H₀: Heights do not follow a normal distribution with mean 166.55 and standard deviation 12.46,H_A: Heights follow a normal distribution with mean 166.55 and standard deviation 12.46
C) H₀: Heights follow a normal distribution with mean 166.55 and standard deviation 12.57,H_A: Heights do not follow a normal distribution with mean 166.55 and standard deviation 12.57
D) H₀: Heights do not follow a normal distribution with mean 166.55 and standard deviation 12.57,H_A: Heights follow a normal distribution with mean 166.55 and standard deviation 12.57

Question 78

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. At the 5% significance level,the critical value is ________.

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

Question 79

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

A) H₀: Age group and income are dependent;H_A: Age group and income are independent
B) H₀: Age group and income are mutually exclusive;H_A: Age group and income are not mutually exclusive
C) H₀: Age group and income are not mutually exclusive;H_A: Age group and income are mutually exclusive
D) H₀: Age group and income are independent;H_A: Age group and income are dependent

Question 80

In the following table,individuals are cross-classified by their age group and income level. 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