Deck 11: Chi-Square Tests

Question 1

For a goodness-of-fit test,the frequencies that we would obtain if the null hypothesis is true are the:

A)expected frequencies
B)subjective frequencies
C)objective frequencies
D)observed frequencies

Answer 1

expected frequencies

Question 2

Which of the following is not a characteristic of a multinomial experiment?

A)It consists of n identical trials.
B)Each trial results in one of the k possible outcomes where k is a number greater than 2.
C)The trials are dependent.
D)The probabilities of various outcomes remain constant for each trial.

Answer 2

The trials are dependent.

Question 3

For a goodness-of-fit test,when n is the sample size and p is the probability of a category occurring,we calculate the expected frequency for a category by:

A)
B)
C)
D)

Answer 3

Question 4

Which of the following is not a characteristic of a multinomial experiment?

A)It consists of n identical trials.
B)Each trial results in one of two possible outcomes.
C)The trials are independent.
D)The probabilities of various outcomes remain constant for each trial.

Question 5

A goodness-of-fit test:

A)is always a right-tailed test
B)is always a left-tailed test
C)is always a two-tailed test
D)can be a right-tailed,left-tailed,or a two-tailed test

Question 6

For a goodness-of-fit test,the sample size should be large enough so that the:

A)observed frequency for each category is at least 10
B)expected frequency for each category is at least 10
C)observed frequency for each category is at least 5
D)expected frequency for each category is at least 5

Question 7

For very large degrees of freedom,the chi-square distribution becomes:

A)symmetric
B)skewed to the right
C)skewed to the left
D)rectangular

Question 8

What is the chi-square value for 19 degrees of freedom and a 0.025 area in the right tail?

A)30.144
B)32.852
C)8.907
D)10.117

Question 9

For a chi-square distribution curve with 3 or more degrees of freedom,the peak occurs at the point:

A)x = 10
B)x = degrees of freedom minus 1
C)x = degrees of freedom minus 2
D)n - x

Question 10

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.What is the expected frequency for the second category?

Question 11

Which of the following is not a characteristic of a multinomial experiment?

A)It consists of two identical trials.
B)Each trial results in one of the k possible outcomes where k is a number greater than 2.
C)The trials are independent.
D)The probabilities of various outcomes remain constant for each trial.

Question 12

The parameter(s)of the chi-square distribution is/are:

A)the sample size
B)degrees of freedom
C)n and x
D)n,x,and p

Question 13

What is the chi-square value for 14 degrees of freedom and a .05 area in the right tail?

A)21.604
B)26.119
C)23.685
D)29.141

Question 14

For a goodness-of-fit test,the frequencies obtained from the performance of an experiment are the:

A)expected frequencies
B)subjective frequencies
C)objective frequencies
D)observed frequencies

Question 15

What is the chi-square value for 9 degrees of freedom and a .01 area in the left tail?

A)21.666
B)-21.666
C)2.088
D)-2.088

Question 16

For a goodness-of-fit test with the number of categories equal to k and sample size equal to n,the degrees of freedom are:

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

Question 17

Which of the following is not a characteristic of a multinomial experiment?

A)It consists of n identical trials.
B)Each trial results in one of the k possible outcomes where k is a number greater than 2.
C)The trials are independent.
D)The probabilities of various outcomes are different for each trial.

Question 18

For small degrees of freedom,the chi-square distribution is:

A)symmetric
B)skewed to the right
C)skewed to the left
D)rectangular

Question 19

What is the chi-square value for 12 degrees of freedom and a 0.10 area in the left tail?

A)6.304
B)-6.304
C)18.549
D)-18.549

Question 20

A chi-square distribution assumes:

A)negative values only
B)positive values only
C)nonnegative values only
D)all values

Question 21

Use the following to answer questions :
The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week.What is the expected number of crimes reported on a Thursday?

Question 22

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same.What is the expected frequency for the fourth category?

Question 23

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same.The significance level is 5%.What is the critical value of chi-square?

A)11.070
B)12.833
C)11.143
D)9.488

Question 24

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category,30% belong to the second category,20% belong to the third category,and 10% belong to the fourth category.What are the degrees of freedom for this test?

Question 25

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category,30% belong to the second category,20% belong to the third category,and 10% belong to the fourth category.The significance level is 10%.What is the critical value of chi-square?

A)9.488
B)7.815
C)7.779
D)6.251

Question 26

Use the following to answer questions :
You ask 100 persons what color of car they like the most.The table below lists the observed frequencies for such a survey.

The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,25% like blue cars,20% like red cars,10% like white cars,and 35% like other colors.What is the expected frequency for red cars?

Question 27

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.What are the degrees of freedom for this test?

Question 28

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.What is the value of the test statistic,rounded to three decimal places?

Question 29

Use the following to answer questions :
You ask 100 persons what color of car they like the most.The table below lists the observed frequencies for such a survey.

The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,25% like blue cars,20% like red cars,10% like white cars,and 35% like other colors.The significance level is 2.5%.What is the critical value of chi-square?

A)9.488
B)11.143
C)12.833
D)11.070

Question 30

Use the following to answer questions :
You ask 100 persons what color of car they like the most.The table below lists the observed frequencies for such a survey.

The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,25% like blue cars,20% like red cars,10% like white cars,and 35% like other colors.The expected frequencies for the various colors are:

Question 31

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category,30% belong to the second category,20% belong to the third category,and 10% belong to the fourth category.What is the expected frequency for the fourth category?

Question 32

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.The expected frequencies for the four categories are:

Question 33

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that 40% of all elements of the population belong to the first category,30% belong to the second category,20% belong to the third category,and 10% belong to the fourth category.The expected frequencies for the four categories are:

Question 34

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.What is the value of the test statistic,rounded to three decimal places?

Question 35

Use the following to answer questions :
You ask 100 persons what color of car they like the most.The table below lists the observed frequencies for such a survey.

The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,25% like blue cars,20% like red cars,10% like white cars,and 35% like other colors.What are the degrees of freedom for this test?

Question 36

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same.The expected frequencies for the five categories are:

Question 37

Use the following to answer questions :
You ask 100 persons what color of car they like the most.The table below lists the observed frequencies for such a survey.

The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,25% like blue cars,20% like red cars,10% like white cars,and 35% like other colors.What is the value of the test statistic,rounded to three decimal places?

Question 38

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same.What is the value of the test statistic,rounded to three decimal places?

Question 39

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same.The significance level is 1%.What is the critical value of chi-square?

A)13.277
B)11.345
C)12.838
D)14.860

Question 40

Use the following to answer questions :
The table below lists the observed frequencies for all four categories for an experiment.

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the five categories is the same.What are the degrees of freedom for this test?

Question 41

For a chi-square test of homogeneity,a contingency table with 5 rows and 6 columns has how many degrees of freedom?

Question 42

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

To perform a chi-square test of independence for this contingency table at the 1% significance level,what is the critical value of chi-square?

A)7.879
B)6.635
C)10.597
D)9.210

Question 43

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

For a chi-square test of independence for this contingency table,what are the expected frequencies for the second column,rounded to two decimal places?

Question 44

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

For a chi-square test of independence for this contingency table,what are the observed frequencies for the first row?

Question 45

Use the following to answer questions :
The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week.What are the degrees of freedom for this test?

Question 46

A chi-square test of independence is about the independence of:

A)two means
B)two proportions
C)two characteristics presented in a contingency table
D)means of several populations

Question 47

A chi-square test of homogeneity is about:

A)testing the null hypothesis that two samples are homogeneous
B)testing the null hypothesis that two proportions are homogeneous
C)the independence of two characteristics presented in a contingency table
D)testing the null hypothesis that the proportions of elements with certain characteristics in two or more different populations are the same

Question 48

Use the following to answer questions :
The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week.The significance level is 10%.What is the critical value of chi-square?

A)12.017
B)14.067
C)10.645
D)12.592

Question 49

For a chi-square test of independence,a contingency table with 2 rows and 2 columns has how many degrees of freedom?

Question 50

For a chi-square test of independence,a contingency table with 7 rows and 8 columns has how many degrees of freedom?

Question 51

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

For a chi-square test of independence for this contingency table,what are the observed frequencies for the second column?

Question 52

A chi-square test of homogeneity:

A)is always a right-tailed test
B)is always a left-tailed test
C)is always a two-tailed test
D)can be a right-tailed,a left-tailed,or a two-tailed test

Question 53

A chi-square test of independence:

A)is always a right-tailed test
B)is always a left-tailed test
C)is always a two-tailed test
D)can be a right-tailed,a left-tailed,or a two-tailed test

Question 54

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

For a chi-square test of independence for this contingency table,what are the expected frequencies for the first row,rounded to two decimal places?

Question 55

Use the following to answer questions :
The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week.What is the value of the test statistic?

Question 56

For a chi-square test of independence,what are the degrees of freedom?

A)sample size minus one
B)sample size minus two
C)(R-1)(C-1)where R is the number of rows and C is the number of columns in the contingency table
D)(n-1)(k-1)where n is the sample size and k is the number of categories

Question 57

Use the following to answer questions :
The table below lists the number of crimes reported at a police station on each day of the week for the past three months.

The null hypothesis for the goodness-of-fit test is that the number of crimes reported at this police station is the same for each day of the week.The expected frequencies for each of the seven days are:

Question 58

For a chi-square test of homogeneity,a contingency table with 7 rows and 9 columns has how many degrees of freedom?

Question 59

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

For a chi-square test of independence for this contingency table,what is the number of degrees of freedom?

Question 60

For a chi-square test of homogeneity,what are the degrees of freedom?

A)sample size minus one
B)sample size minus two
C)(R-1)(C-1)where R is the number of rows and C is the number of columns in the contingency table
D)(n-1)(k-1)where n is the sample size and k is the number of categories

Question 61

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

For a chi-square test of homogeneity for this contingency table,what are the observed frequencies for the second column?

Question 62

Use the following to answer questions :
A random sample of 25 elements selected from a population produced a variance equal to 3.937.Assume that the population is normally distributed.
Based on this sample,the 95% confidence interval for the population standard deviation,rounded to three decimal places,is:

Question 63

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

To perform a chi-square test of independence for this contingency table,what is the value of the chi-square test statistic (rounded to three decimal places)?

Question 64

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

To perform a chi-square test of independence for this contingency table at the 5% significance level,what is the critical value of chi-square?

A)5.991
B)7.378
C)3.841
D)5.024

Question 65

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

For a chi-square test of independence for this contingency table,what are the observed frequencies for the first column?

Question 66

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

For a chi-square test of independence for this contingency table,what are the observed frequencies for the second row?

Question 67

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

For a chi-square test of independence for this contingency table,what are the expected frequencies for the first column,rounded to two decimal places?

Question 68

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

To perform a chi-square test of homogeneity for this contingency table,what is the value of the chi-square test statistic (rounded to three decimal places)?

Question 69

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

For a chi-square test of independence for this contingency table,what is the number of degrees of freedom?

Question 70

Use the following to answer questions :
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.The table below gives a two-way classification for these adults.

For a chi-square test of independence for this contingency table,what are the expected frequencies for the second row,rounded to two decimal places?

Question 71

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

For a chi-square test of homogeneity for this contingency table,what are the expected frequencies for the second column,rounded to two decimal places?

Question 72

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

To perform a chi-square test of homogeneity for this contingency table at the 10% significance level,what is the critical value of chi-square?

A)5.991
B)4.605
C)3.841
D)2.706

Question 73

Use the following to answer questions :
A random sample of 20 elements selected from a population produced a variance equal to 11.072.Assume that the population is normally distributed.
Based on this sample,the 90% confidence interval for the population variance,rounded to three decimal places,is:

Question 74

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

For a chi-square test of homogeneity for this contingency table,what are the expected frequencies for the first row,rounded to two decimal places?

Question 75

Use the following to answer questions :
You observe 100 randomly selected college students to find out whether they arrive on time or late for their classes.The table below gives a two-way classification for these students.

To perform a chi-square test of independence for this contingency table,what is the value of the chi-square test statistic (rounded to three decimal places)?

Question 76

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

For a chi-square test of homogeneity for this contingency table,what is the number of degrees of freedom?

Question 77

Use the following to answer questions :
A random sample of 16 elements selected from a population produced a variance equal to 7.954.Assume that the population is normally distributed.
Based on this sample,the 99% confidence interval for the population standard deviation,rounded to three decimal places,is:

Question 78

Use the following to answer questions :
A clinic administers two drugs to two groups of randomly assigned patients to cure the same disease: 70 patients received Drug I and 80 patients received Drug II.The following table gives the information about the numbers of patients cured and those not cured by each of these two drugs.

For a chi-square test of homogeneity for this contingency table,what are the observed frequencies for the first row?

Question 79

Use the following to answer questions :
A random sample of 25 elements selected from a population produced a variance equal to 3.937.Assume that the population is normally distributed.
Based on this sample,the 95% confidence interval for the population variance,rounded to three decimal places,is:

Question 80

Use the following to answer questions :
A random sample of 16 elements selected from a population produced a variance equal to 7.954.Assume that the population is normally distributed.
Based on this sample,the 99% confidence interval for the population variance,rounded to three decimal places,is: