Deck 15: Nonparametric Methods: Goodness-Of-Fit Tests

Question 1

The use of the chi-square statistic would be permissible in the following goodness-of-fit test.

Answer 1

False

Question 2

To test the null hypothesis that a set of sample data is normally distributed, we compare an expected normal distribution of the data to an observed distribution of the data.

Answer 2

True

Question 3

The shape of the chi-square distribution depends on the size of the sample.

Answer 3

False

Question 4

The null hypothesis in the goodness-of-fit test is __________.

Question 5

Nonparametric tests require no assumptions about the shape of the population distribution.

Question 6

The claim that "male and female students at Coastal Carolina University prefer different parking lots on campus" is an example of a chi-square null hypothesis.

Question 7

As the degrees of freedom increase, the shape of a chi-square distribution approaches a ______________ distribution.

Question 8

The computed value of a chi-square statistic is always positive because the numerator is the difference between the observed frequencies and the expected frequencies ______________.

Question 9

A scatter plot is a useful graphical method to determine if a set of sample data is from a normal population.

Question 10

For a goodness-of-fit test, the following are possible null and alternate hypotheses:
H₀: Sales are uniformly distributed among the five locations.
H₁: Sales are not uniformly distributed among the five locations.

Question 11

The chi-square distribution is positively skewed.

Question 12

For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.

Question 13

A t-statistic is useful for computing an expected normal distribution.

Question 14

An F distribution is useful for testing the null hypothesis that a set of sample data is normally distributed.

Question 15

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

Question 16

A chi-square goodness-of-fit test is used to determine how well an observed distribution fits an _________ distribution.

Question 17

The chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom.

Question 18

There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on.

Question 19

The lowest level of measurement for a chi-square goodness-of-fit test is the ______________ level.

Question 20

In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations "fits" an expected distribution of observations.

Question 21

The test statistic for a goodness-of-fit test for unequal expected frequencies is a __________ statistic.

Question 22

In a contingency table, the decision to reject the null hypothesis is based on a __________ test statistic.

Question 23

When testing a goodness-of-fit null hypothesis, and there are extremely large differences between observed and expected frequencies, the null hypothesis should be ___________.

Question 24

To test a hypothesis that a frequency distribution for sample data is normally distributed, class limits are transformed using a ____________.

Question 25

The Anderson-Darling test for normality compares a cumulative normal distribution to a cumulative distribution of the ___________ data.

Question 26

If the computed value of a chi-square statistic is greater than the critical value, the null hypothesis is ________.

Question 27

Contingency table analysis can be used to test for a relationship between two _________ scale variables.

Question 28

To verify that a frequency distribution for sample data is normally distributed, the expected frequencies are computed using probabilities from a _____________ distribution.

Question 29

A contingency table shows the frequencies for three levels of income with gender. There are ______ degrees of freedom to test the null hypothesis that income and gender are independent.

Question 30

In a contingency table, multiplying the row total by the column total and dividing by the ___________ computes the expected frequency for a cell.

Question 31

The Anderson-Darling test for normality tests a null hypothesis that the sample data are ______ distributed.

Question 32

To test a hypothesis to verify that an observed frequency distribution data is normally distributed, the expected frequencies are _______________ distributed.

Question 33

If the significance level for an Anderson-Darling test for normality is 0.05 and the p-value is 0.001, the null hypothesis is rejected and we conclude that the data _________ normally distributed.

Question 34

For hypothesis tests using a chi-square statistic, the rejection region is in the _____________ tail of the chi-square distribution.

Question 35

For any goodness-of-fit test, the null hypothesis is that there is ____ difference between the expected and observed distributions.

Question 36

In a contingency table analysis, the decision to reject the null hypothesis is based on a __________ test statistic.

Question 37

The shape of the chi-square distribution is _________________.

Question 38

The degrees of freedom for a chi-square goodness-of-fit test is equal to ______________.

Question 39

To verify that an observed frequency distribution is normally distributed, a ________ statistic is used to test the hypothesis that the sample data is normally distributed.

Question 40

A question has these possible responses-excellent, very good, good, fair, and unsatisfactory. What are the degrees of freedom for a goodness-of-fit test to test the hypothesis that responses are uniformly distributed?

A)0
B)2
C)4
D)5

Question 41

The chi-square statistic has __________.

A)One distribution
B)Two distributions
C)A family of distributions
D)A uniform distribution

Question 42

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be _______________.

A)That willow green is preferred over the other colors
B)That there is no preference between the colors
C)That any one color is preferred over the other colors
D)Impossible to determine

Question 43

A distributor of personal computers has five locations in a city. In the year's first quarter, the sales in units were: For a goodness-of-fit test that sales were the same for all locations, what is the critical value at the 0.01 level of risk?

A)7.779
B)15.033
C)13.277
D)5.412

Question 44

For any chi-square goodness-of-fit test, the number of degrees of freedom is found by ______.

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

Question 45

For people released from prison, the following table shows their adjustment to civilian life and place of residence. What is the critical value for this contingency table at the 0.01 level of significance?

A)9.488
B)2.070
C)11.345
D)13.277

Question 46

The contingency table for a sample of corporate executives classified by educational level and the social activity follows. What does the expected frequency for the "above average" social activity and "high school" education equal?

A)9.50
B)60.00
C)22.50
D)28.50

Question 47

What is our decision for a goodness-of-fit test with a computed chi-square value of 1.273 and a critical value of 13.388?

A)Do not reject the null hypothesis.
B)Reject the null hypothesis.
C)Unable to reject or not reject the null hypothesis based on data.
D)We should take a larger sample.

Question 48

What is the decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed chi-square value is 6.079?

A)Fail to reject the null hypothesis; the difference is probably due to sampling error.
B)Reject the null hypothesis.
C)Fail to reject the alternate hypothesis.
D)Too close; reserve judgment.

Question 49

What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?

A)3.841
B)5.991
C)7.815
D)11.070

Question 50

Which of the following assumptions is necessary to apply a goodness-of-fit test?

A)The population must be normally distributed.
B)The data are measured with a nominal or ordinal scale.
C)The population variance must be known.
D)The population mean must be known.

Question 51

The following table classifies 100 individuals using two variables, gender and college attended. What is this two-way classification called?

A)Goodness-of-fit test
B)Frequency table
C)ANOVA table
D)Contingency table

Question 52

A sample of 100 production workers is obtained. The workers are classified by gender (male, female) and by age (under 20, 20-29, 30-39, and 40 or over). How many degrees of freedom are there?

A)0
B)3
C)6
D)5

Question 53

Which chi-square distribution would be closest to a normal distribution?

A)The distribution with 3 degrees of freedom.
B)The distribution with 12 degrees of freedom.
C)The distribution with 15 degrees of freedom.
D)The distribution with 9 degrees of freedom.

Question 54

The chi-square distribution becomes more symmetrical as the ____________.

A)Number of variables increases
B)The chi-square value increases
C)Degrees of freedom decrease
D)Degrees of freedom increase

Question 55

Which of the following statements is correct regarding the goodness-of-fit test?

A)Variables are based on the nominal measurement scale.
B)Population must be normal.
C)All the expected frequencies must be equal.
D)All the expected frequencies must be unequal.

Question 56

For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are __________.

A)Linear
B)Curvilinear
C)Not related
D)Related

Question 57

The chi-square statistic _______________.

A)Is greater than or equal to zero
B)Is less than or equal to zero
C)Can be any value
D)Is equal to zero

Question 58

The chi-square distribution is _____________.

A)Positively skewed
B)Negatively skewed
C)Normally distributed
D)Uniformly distributed

Question 59

What are the degrees of freedom for a contingency table analysis?

A)n - 1
B)Rows - Columns
C)(Rows) × (Columns)
D)(Rows - 1) × (Columns - 1)

Question 60

Which of the following statements is correct regarding the chi-square distribution?

A)The distribution is negatively skewed.
B)Chi-square is based on two sets of degrees of freedom, one for the numerator and one for the denominator.
C)The shape of the distribution is based on the degrees of freedom.
D)The variance of the distribution is equal to one.

Question 61

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. What is the value of the chi-square test statistic?

A)100
B)83.67
C)50
D)4.94

Question 62

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The null hypothesis for the analysis is __________________________.

A)There is no relationship between social activity and education.
B)The correlation between social activity and education is zero.
C)As social activity increases, education increases.
D)The mean of social activity equals the mean of education.

Question 63

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are: What is the critical value of chi-square with α = 0.05?

A)11.070
B)12.592
C)13.388
D)15.033

Question 64

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are: What kind of frequencies are the numbers 12, 9, 11, 10, 9, and 9 called?

A)Acceptance frequencies
B)Critical frequencies
C)Expected frequencies
D)Observed frequencies

Question 65

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The degrees of freedom for the analysis are __________.

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

Question 66

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test statistic for the analysis is a(n) __________.

A)F-statistic
B)t-statistic
C)Chi-square statistic
D)z-statistic

Question 67

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: The degrees of freedom for the analysis are ________.

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

Question 68

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are: What is the calculated value of chi-square?

A)1.0
B)0.5
C)0.8
D)8.0

Question 69

When determining how well an observed set of frequencies fit an expected set of frequencies, what is the test statistic?

A)F-statistic
B)t-statistic.
C) statistic
D)z-statistic

Question 70

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Using 0.05 as the significance level, what is the critical value for the test statistic?

A)9.488
B)5.991
C)7.815
D)3.841

Question 71

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Based on the analysis, what can be concluded?

A)Social activity and education are correlated.
B)Social activity and education are not related.
C)Social activity and education are related.
D)No conclusion is possible.

Question 72

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students: The null hypothesis for the analysis is ____________.

A)There is no relationship between gender and speeding
B)The correlation between driving behavior and gender is zero
C)As driving behavior increases, gender increases
D)The mean of driving behavior equals the mean of gender

Question 73

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are: What is the expected frequency?

A)9
B)10
C)11
D)12

Question 74

In a goodness-of-fit test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the ________________.

A)Computed chi-square is less than the critical value
B)Difference between the observed and expected frequencies is significantly large
C)Difference between the observed and expected frequencies is small
D)Difference between the observed and expected frequencies occurs by chance

Question 75

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: What is the value of the test statistic?

A)83.67
B)9.890
C)50
D)4.94

Question 76

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: Using 0.05 as the significance level, what is the critical value for the test statistic?

A)9.488
B)5.991
C)7.815
D)3.841

Question 77

Which of the following can be used to test the hypothesis that two nominal variables are related?

A)A contingency table analysis
B)A goodness-of-fit
C)ANOVA
D)A regression analysis

Question 78

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test to analyze the relationship between social activity and education is __________.

A)A regression analysis
B)An analysis of variance
C)A contingency table analysis
D)A goodness-of-fit test

Question 79

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. Use the 0.01 level of significance. The sample results are: How many degrees of freedom are there?

A)0
B)3
C)4
D)5

Question 80

The computed chi-square value is positive because the difference between the observed and expected frequencies is _____________.

A)Squared
B)Linear
C)Uniform
D)Always positive