Deck 17: Nonparametric Methods: Goodness-Of-Fit Tests

Question 1

The chi-square distribution is positively skewed.

Answer 1

True

Question 2

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

Answer 2

Expected

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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 8

The shape of the chi-square distribution changes for each number of degrees of freedom.

Question 9

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 10

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.

Question 11

What is the null hypothesis in the goodness-of-fit test? ____________

Question 12

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

Question 13

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

Question 14

What is the lowest level of data for which the chi-square goodness-of-fit test is appropriate? ______________

Question 15

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

Question 16

A F-test is useful for testing the null hypothesis that a set of sample data is normally distributed.

Question 17

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

Question 18

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 19

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 20

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

Question 21

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

Question 22

If the computed value of a chi-square statistic is greater than the critical value, what is the decision regarding the null hypothesis? _________

Question 23

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

Question 24

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

Question 25

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

Question 26

For contingency table test of independence, the formula to compute the degrees of freedom is ___________________________________

Question 27

What is the shape of the chi-square distribution? ___________________

Question 28

The Anderson-Darling tests a null hypothesis that the sample data are _____________ distributed.

Question 29

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

Question 30

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

Question 31

When testing a goodness-of-fit null hypothesis, and there are extremely large differences between observed and expected frequencies, what decision should be made? ____________

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

To verify that a frequency distribution for sample data is normally distributed, a _____________ statistic is used to test the hypothesis that the sample data is normally distributed.

Question 39

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

Question 40

What is the degree of freedom for a chi-square goodness-of-fit test? ____________________________

Question 41

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 42

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

A) Data may be of nominal scale
B) Population must be normal
C) All the expected frequencies must be equal
D) All the expected frequencies must be unequal

Question 43

A question has these possible choices-excellent, very good, good, fair and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results?

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

Question 44

The following table classifies an individual in two ways-by gender and by college attended. What is this two-way classification called?

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

Question 45

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 value is 6.079?

A) The difference is probably due to sampling error; do not reject the null hypothesis
B) Not due to chance; reject the null hypothesis
C) Not due to chance; do not reject the alternate hypothesis
D) Too close; reserve judgment

Question 46

To analyze data cross-classified in a contingency table, how are the degrees of freedom computed?

A) N - 1
B) Rows - Columns
C) (Rows) x (Columns)
D) (Rows - 1) x (Columns - 1)

Question 47

The educational level and the social activity of a sample of executives follow. 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 48

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 49

What is our decision for a goodness-of-fit test with a computed value of chi-square 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) Should take a larger sample

Question 50

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) willow green is preferred over the other colors.
B) that there is no preference between the colors.
C) any one color is preferred over the other colors.
D) impossible to determine.

Question 51

The chi-square statistic has

A) one distribution.
B) two distributions.
C) a family of distributions.
D) a uniform distribution.

Question 52

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

A) 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) Its shape is based on the degrees of freedom.
D) The variance is equal to one.

Question 53

The chi-square distribution becomes more symmetrical as

A) number of variables increase.
B) the chi-square value increases.
C) degrees of freedom decrease.
D) degrees of freedom increase.

Question 54

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

A) Normal population is required.
B) The data are measured with a nominal or ordinal scale.
C) Population variance must be known.
D) Both "a" and "c".

Question 55

The chi-square distribution is

A) positively skewed.
B) negatively skewed.
C) normally distributed.
D) negatively or positively skewed.

Question 56

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 57

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

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

Question 58

A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows: 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 59

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 60

Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution?

A) 3 degrees
B) 12 degrees
C) 15 degrees
D) All would

Question 61

A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested 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 62

A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested 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
B) Critical value
C) Expected
D) Observed

Question 63

A recent study of the relationship between social activity and education 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 64

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 65

A recent study of the relationship between social activity and education 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 66

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.

Question 67

A recent study of the relationship between social activity and education showed the following results. The appropriate test statistic for the analysis is a:

A) F-statistic
B) T-statistic
C) Chi-square statistic
D) Z-statistic

Question 68

A recent study of the relationship between social activity and education 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 69

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

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

Question 70

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. 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 driving behavior.
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 71

A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested 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 72

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

A) a contingency table.
B) a chi-square table.
C) an ANOVA table.
D) a scatter diagram.

Question 73

A recent study of the relationship between social activity and education showed the following results. The appropriate test to analyze the relationship between social activity and education is:

A) Regression analysis
B) Analysis of variance
C) Contingency table analysis
D) Goodness-of-fit

Question 74

A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested 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 $\alpha$ = 0.05?

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

Question 75

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 76

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested 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 is:

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

Question 77

A recent study of the relationship between social activity and education showed the following results. The degrees of freedom for the analysis is:

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

Question 78

A recent study of the relationship between social activity and education showed the following results. What is the value of the test statistic?

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

Question 79

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 80

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested 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