Deck 15: Chi-Square Tests

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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 7

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

Question 8

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

Question 9

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

Question 10

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 11

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.

Question 12

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

Question 13

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 14

A chi-square distribution is always skewed right.

Question 15

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

Question 16

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 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

The Poisson goodness-of-fit test is inappropriate for continuous data.

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

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 25

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 26

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

Question 27

Probability plots are used to test the assumption of normality.

Question 28

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

Question 29

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

Question 30

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 31

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

Question 32

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

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

Question 35

A probability plot usually allows outliers to be detected.

Question 36

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

Question 37

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 38

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

Question 39

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

Question 40

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

Question 41

An operations analyst counted the number of arrivals per minute at an ATM in each of 30 randomly chosen minutes.The results were: 0,3,3,2,1,0,1,0,0,1,1,1,2,1,0,1,0,1,2,1,1,2,1,0,1,2,0,1,0,1.For the Poisson goodness-of-fit test,what is the expected frequency of the data value X = 1?

A) Impossible to determine.
B) 11.04
C) 1.00
D) 2.47

Question 42

A proofreader checked 160 ads for grammatical errors.The distribution obtained is shown: 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 43

To determine how well an observed set of frequencies fits an expected set of frequencies from a Poisson distribution we must estimate:

A) no parameters.
B) one parameter (λ).
C) two parameters (μ,σ).
D) three parameters (μ,σ,n).

Question 44

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 45

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 46

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

Question 47

An operations analyst counted the number of arrivals per minute at a bank ATM in each of 30 randomly chosen minutes.The results were: 0,3,3,2,1,0,1,0,0,1,1,1,2,1,0,1,0,1,2,1,1,2,1,0,1,2,0,1,0,1.Which goodness-of-fit test would you recommend?

A) Uniform.
B) Poisson.
C) Normal.
D) Binomial.

Question 48

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

A) 55.
B) 79.
C) 85.

Question 49

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 50

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 51

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 52

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 following frequencies: 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 53

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

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 54

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 55

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 56

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,degrees of freedom would be:

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

Question 57

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 following frequencies: Find the chi-square test statistic for a hypothesis of independence.

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

Question 58

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 59

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 60

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 61

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.

Question 62

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: What is the value of the test statistic?

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

Question 63

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 64

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,degrees of freedom would be:

A) 20.
B) 12.
C) 399.

Question 65

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

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

Question 66

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,the critical value for α = .05 is:

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

Question 67

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. Assuming independence,the expected frequency of satisfied hourly employees is:

A) 80.
B) 90.
C) 75.

Question 68

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 critical value for α = .01 is:

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

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,degrees of freedom would be:

A) 2.
B) 9.
C) 4.

Question 70

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)

Question 71

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 follows: 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 72

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 73

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 74

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: 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 75

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 appropriate conclusion would be:

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

Question 76

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 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: Using α = .05,what 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 78

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 79

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,the expected frequency of very uncertain students with 60 credits or more is:

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

Question 80

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: The expected frequency for the shaded cell is:

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