Deck 14: Chi-Square Tests

Question 1

A chi-square distribution is always skewed right.

Answer 1

True

Question 2

A chi-square test for independence is called a distribution-free test since the test is based on categorical data rather than on populations that follow any particular distribution.

Answer 2

True

Question 3

In a chi-square test for independence,observed frequencies must be at least 5 in every cell.

Answer 3

False

Question 4

Observed frequencies in a chi-square goodness-of-fit test for normality may be less than 5,or even 0,in some cells,as long as the expected frequencies are large enough.

Question 5

The shape of the chi-square distribution depends only on its degrees of freedom.

Question 6

The null hypothesis for a chi-square test on a contingency table is that the variables are dependent.

Question 7

The chi-square test is unreliable when there are any cells with small observed frequency counts.

Question 8

In a chi-square test for independence,expected frequencies must be integers (or rounded to the nearest integer).

Question 9

In a chi-square test for independence,observed and expected frequencies must sum across to the same row totals and down to the same column totals.

Question 10

In a hypothesis test using chi-square,if the null hypothesis is true,the sample value of the sample chi-square test statistic will be exactly zero.

Question 11

In a chi-square test of a 5 × 5 contingency table at α = .05,the critical value is 37.65.

Question 12

In samples drawn from a population in which the row and column categories are independent,the value of the chi-square test statistic will be zero.

Question 13

Cochran's Rule requires observed frequencies of 5 or more in each cell of a contingency table.

Question 14

If two variables are independent,we would anticipate a chi-square test statistic close to zero.

Question 15

A large negative chi-square test statistic would indicate that the null hypothesis should be rejected.

Question 16

The chi-square test can only be used to assess independence between two variables.

Question 17

The chi-square test is based on an analysis of frequencies.

Question 18

The null hypothesis for a chi-square contingency test of independence for two variables always assumes that the variables are independent.

Question 19

The chi-square test for independence is a nonparametric test (no parameters are estimated).

Question 20

The degrees of freedom in a 3 × 4 chi-square contingency table would equal 11.

Question 21

The Kolmogorov-Smirnov and Anderson-Darling tests are based on the ECDF (Empirical Cumulative Distribution Function).

Question 22

In an ECDF test for goodness-of-fit,the n observations are grouped into categories rather than being treated individually.

Question 23

Goodness-of-fit tests using the ECDF (Empirical Cumulative Distribution Function)compare the actual cumulative frequencies with expected cumulative frequencies for each observation under the assumption that the data came from the hypothesized distribution.

Question 24

In a chi-square goodness-of-fit test,we gain one degree of freedom if n increases by 1.

Question 25

ECDF tests have an advantage over the chi-square goodness-of-fit test on frequencies because an ECDF test treats observations individually.

Question 26

For a chi-square goodness-of-fit test for a uniform distribution with 7 categories,we would use the critical value for 6 degrees of freedom.

Question 27

The Anderson-Darling test is used to test the assumption of normality.

Question 28

For a chi-square goodness-of-fit test for a uniform distribution with 5 categories,we would use the critical value for 4 degrees of freedom.

Question 29

An attraction of the Anderson-Darling test is that it is fairly easy to do without a computer.

Question 30

Probability plots are used to test the assumption of normality.

Question 31

In a chi-square goodness-of-fit test,a small p-value would indicate a good fit to the hypothesized distribution.

Question 32

A probability plot usually allows outliers to be detected.

Question 33

For a chi-square goodness-of-fit test for a normal distribution using 7 categories with estimated mean and standard deviation,we would use the critical value for 4 degrees of freedom.

Question 34

In a goodness-of-fit test,a linear probability plot suggests that the null hypothesis should be rejected.

Question 35

An attraction of the Kolmogorov-Smirnov test is that it is fairly easy to do without a computer.

Question 36

In a test for a uniform distribution with k categories,the expected frequency is n/k in each cell.

Question 37

For a chi-square goodness-of-fit test for a normal distribution using 8 categories with estimated mean and standard deviation,we would use the critical value for 7 degrees of freedom.

Question 38

When raw data are available,ECDF tests usually surpass the chi-square test in their ability to detect departures from the distribution specified in the null hypothesis.

Question 39

In a chi-square goodness-of-fit test,we lose one degree of freedom for each parameter estimated.

Question 40

In a chi-square goodness-of-fit test,a sample of n observations has n − 1 degrees of freedom.

Question 41

Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications.A sample of one day's output of kortholts from the Melodic Kortholt Company showed the frequencies shown below. Find the p-value for the chi-square test statistic for a hypothesis of independence.

A)Less than .01
B)Between .01 and .025
C)Between .025 and .05
D)Greater than .05

Question 42

The table below is a tabulation of opinions of employees of Axolotl Corporation,who were sampled at random from pay records and asked to complete an anonymous job satisfaction survey. For a chi-square test of independence,which is the critical value for α = .01?

A)9.210
B)4.605
C)11.34
D)16.81

Question 43

The table below is a tabulation of opinions of employees of Axolotl Corporation,who were sampled at random from pay records and asked to complete an anonymous job satisfaction survey,with the results shown below. Assuming independence,the expected frequency of satisfied hourly employees is

A)80
B)90
C)75
D)60

Question 44

The table below is a tabulation of opinions of employees of Axolotl Corporation,who were sampled at random from pay records and asked to complete an anonymous job satisfaction survey. For a chi-square test of independence,the degrees of freedom would be

A)2
B)3
C)4
D)6

Question 45

In a chi-square test of independence,the number of degrees of freedom equals the

A)number of observations minus one.
B)number of categories minus one.
C)number of rows minus one times the number of columns minus one.
D)number of sample observations minus the missing observations.

Question 46

Which of the following is not a potential solution to the problem that arises when not all expected frequencies are 5 or more in a chi-square test for independence?

A)Combine some of the columns.
B)Combine some of the rows.
C)Increase the sample size.
D)Add more rows or columns.

Question 47

If samples are drawn from a population that is normal,a goodness-of-fit test for normality could yield

A)Type I error but not Type II error.
B)Type II error but not Type I error.
C)either Type I error or Type II error.
D)both Type I and Type II errors.

Question 48

A chi-square test of independence is a one-tailed test.The reason is that

A)we are testing whether the frequencies exceed their expected values.
B)we square the deviations,so the test statistic lies at or above zero.
C)hypothesis tests are one-tailed tests when dealing with sample data.
D)the chi-square distribution is positively skewed.

Question 49

In order to apply the chi-square test of independence,we prefer to have

A)at least 5 observed frequencies in each cell.
B)at least 5 expected observations in each cell.
C)at least 5 percent of the observations in each cell.
D)not more than 5 observations in each cell.

Question 50

Which of these statements concerning a chi-square goodness-of-fit test is correct?

A)It is inapplicable to test for a normal distribution with open-ended top and bottom classes.
B)It is generally a better test than the chi-square test of independence.
C)There is no way to get the degrees of freedom since the right tail goes to infinity.
D)It can be used to test whether a sample follows a specified distribution.

Question 51

A proofreader checked 160 ads for grammatical errors.The sample frequency distribution is shown below. Under the null hypothesis of a uniform distribution,the expected number of times we would get 0 errors is

A)10
B)20
C)30
D)40

Question 52

A proofreader checked 160 ads for grammatical errors.The sample frequency distribution is shown below. A goodness-of-fit test to determine whether this sample came from a uniform distribution would result in a chi-square test statistic of approximately

A)55
B)79
C)85
D)161

Question 53

A proofreader checked 160 ads for grammatical errors.The distribution obtained is shown below. At α = .01,what decision would we reach in a goodness-of-fit test to see whether this sample came from a uniform distribution?

A)Reject the null and conclude the distribution is not uniform.
B)Conclude that there is insufficient evidence to reject the null.
C)No conclusion can be made due to small expected frequencies.
D)No conclusion can be made due to inadequate sample size.

Question 54

A chi-square goodness of fit test for a normal distribution used 40 observations,and the mean and standard deviation were estimated from the sample.The test used six categories.We would use how many degrees of freedom in looking up the critical value for the test?

A)39
B)37
C)5
D)3

Question 55

We sometimes combine two row or column categories in a chi-square test when the

A)observed frequencies are more than 5.
B)observed frequencies are less than 5.
C)expected frequencies are more than 5.
D)expected frequencies are less than 5.

Question 56

A chi-square goodness of fit test for a normal distribution used 60 observations,and the mean and standard deviation were estimated from the sample.The test used seven categories.We would use how many degrees of freedom in looking up the critical value for the test?

A)6
B)4
C)59
D)57

Question 57

Which of these statements concerning a chi-square goodness-of-fit test is correct?

A)Data could be ratio or interval measurements.
B)Population must be normally distributed.
C)All the expected frequencies must be equal.

Question 58

The number of cars waiting at a certain residential neighborhood stoplight is observed at 6:00 a.m.on 160 different days.The observed sample frequencies are shown here. Under the null hypothesis of a uniform distribution,the expected number of days we would see 0 cars is

A)10
B)20
C)30
D)40

Question 59

Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications.A sample of one day's output of kortholts from the Melodic Kortholt Company showed the frequencies shown below. Find the chi-square test statistic for a hypothesis of independence.

A)7.22
B)4.17
C)5.13
D)6.08

Question 60

The critical value in a chi-square test for independence depends on

A)the normality of the data.
B)the variance of the data.
C)the number of categories.
D)the expected frequencies.

Question 61

You want to test the hypothesis that the prime rate and inflation are independent.The following table is prepared for the test on the basis of the results of a random sample,collected in various countries and various time periods shown below. The expected frequency for the shaded cell in row 2 and column 3 is

A)22.5
B)30
C)40
D)40.5

Question 62

Students in an introductory college economics class were asked how many credits they had earned in college,and how certain they were about their choice of major.Their replies are summarized below. Which statement is most nearly correct?

A)The contingency table violates Cochran's Rule.
B)Visual inspection of column frequencies suggests independence.
C)At α = .05 we would easily reject the null hypothesis of independence.
D)At α = .05 we cannot reject he null hypothesis of independence.

Question 63

You want to test the hypothesis that the prime rate and inflation are independent.The following table of frequencies is prepared from a random sample,collected in various countries and various time periods: shown below. Based on an analysis of the data in this table,which conclusion can be made at α = .01?

A)The prime rate and inflation rate are independent.
B)The prime rate and inflation rate are not independent.
C)Small observed frequencies in some cells suggest that no reliable conclusion can be made.
D)Small expected frequencies in some cells suggest that no reliable conclusion can be made.

Question 64

To carry out a chi-square goodness-of-fit test for normality you need at least

A)5 categories altogether.
B)5 observations in each category.
C)5 expected observations in each category.
D)50 samples or more.

Question 65

As an independent project,a team of statistics students tabulated the types of vehicles that were parked in four different suburban shopping malls. For a chi-square test of independence,the critical value for α = .10 is

A)10.64
B)14.68
C)28.41
D)18.55

Question 66

You want to sell your house,and you decide to obtain an appraisal on it.Looking at past data,you discover that actual prices obtained for houses and the appraisals given for them prior to their sale were as shown below. Based on these data we can say that

A)no conclusion is possible without knowing α.
B)appraisal and actual price are not independent at α = .05.
C)appraisal and actual price are independent at any α.
D)the degrees of freedom are insufficient for a decision.

Question 67

Preferences for the type of diet drink from a random sample of 121 shoppers are in the table below.A researcher is interested in determining if there is a relationship between the type of diet drink preferred and the age of the shoppers. In performing a chi-square test of independence on these data,how many degrees of freedom will the test statistic have?

A)1
B)2
C)4
D)6

Question 68

Employees of OxCo Mfg.were surveyed to evaluate the company's pension plan.The table below displays some of the results of the survey. The expected frequency for the shaded cell in row 2 and column 2 in the table would be

A)163
B)158
C)165
D)160

Question 69

Students in an introductory college economics class were asked how many credits they had earned in college and how certain they were about their choice of major.Their replies are summarized below. For a chi-square test of independence,which is the critical value for α = .05?

A)5.991
B)7.815
C)9.488
D)16.92

Question 70

You test a hypothesis of independence of two variables.The number of observations is 500 and you have classified the data into a 4 × 4 contingency table.The test statistic has ________ degrees of freedom.

A)16
B)9
C)499
D)498

Question 71

Students in an introductory college economics class were asked how many credits they had earned in college and how certain they were about their choice of major.Their replies are summarized below. Under the assumption of independence,the expected frequency in the upper left cell is

A)15.09
B)24.00
C)19.72
D)20.22

Question 72

Students in an introductory college economics class were asked how many credits they had earned in college,and how certain they were about their choice of major.Their replies are summarized below. Assuming independence,which is the expected frequency of very uncertain students with 60 credits or more?

A)12.47
B)2.00
C)14.56
D)11.09

Question 73

You want to test the hypothesis that the prime rate and inflation are independent.The following table is prepared for the test on the basis of the results of a random sample,collected in various countries and various time periods,shown below. Using α = .05,which is the critical value of the test statistic that you would use?

A)3.841
B)12.59
C)5.991
D)7.815

Question 74

As an independent project,a team of statistics students tabulated the types of vehicles that were parked in four different suburban shopping malls. For a chi-square test of independence,the degrees of freedom would be

A)20
B)12
C)399
D)6

Question 75

Students in an introductory college economics class were asked how many credits they had earned in college and how certain they were about their choice of major.Their replies are summarized below. For a chi-square test of independence,degrees of freedom would be

A)2
B)9
C)4
D)127

Question 76

Employees of OxCo Mfg.were surveyed to evaluate the company's pension plan.The table below displays some of the results of the survey. Degrees of freedom for this test (shaded cell below the table)would be

A)6
B)7
C)799
D)12

Question 77

You want to test the hypothesis that the prime rate and inflation are independent.The following table is prepared for the test on the basis of the results of a random sample,collected in various countries and various time periods shown below. What is the value of the test statistic?

A)306.25
B)0.00
C)54.44
D)13.61

Question 78

Preferences for the type of diet drink from a random sample of 121 shoppers are in the table below.A researcher is interested in determining if there is a relationship between the type of diet drink preferred and the age of the shoppers. Using α = .025,what is the critical value of the test statistic that you would use in a decision rule to test an appropriate hypothesis?

A)5.02
B)5.99
C)7.38
D)14.45

Question 79

Employees of OxCo Mfg.were surveyed to evaluate the company's pension plan.The table below displays some of the results of the survey. Which is the most appropriate conclusion?

A)Do not reject H0.
B)Reject H0 at α = .10.
C)Reject H0 at α = .05.
D)Reject H0 at α = .01.

Question 80

As an independent project,a team of statistics students tabulated the types of vehicles that were parked in four different suburban shopping malls. Assuming independence,the expected frequency of SUVs in Jamestown is

A)12
B)21
C)75
D)60