Question 1

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.

Accepted Answer

Goodness-of-fit tests are used to determine whether a set of observed frequencies fits a theoretical distribution. This test is used when the data are measured with a nominal or ordinal scale. The other options listed are assumptions for other types of tests.

Question 2

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

Accepted Answer

The answer of A personnel manager is concerned about absenteeism....

Question 3

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

Accepted Answer

The answer of A personnel manager is concerned about absenteeism....

Question 4

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

Accepted Answer

To find the expected frequency for the "above average" social activity and "high school" education, we need to multiply the row and column totals and divide by the sample size.

Expected frequency = (Row total for "high school" education) x (Column total for "above average" social activity) / Sample size

Expected frequency = (40) x (15) / 200 = 3 x 7.5 = 22.50

Therefore, the expected frequency for the "above average" social activity and "high school" education equals 22.50. The best choice is C.

Question 5

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

Accepted Answer

The numbers 12, 9, 11, 10, 9, and 9 represent the actual count of absenteeism on each day of the week, and are therefore considered observed frequencies.

Question 6

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

Accepted Answer

The answer of A sample of 100 production workers is...

Question 7

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

Accepted Answer

A contingency table analysis is used to test the relationship between two nominal variables by comparing observed and expected frequencies. Goodness-of-fit, ANOVA, and regression analysis are more appropriate for testing relationships between continuous or ordinal variables.

Question 8

The chi-square statistic has __________.
A) One distribution
B) Two distributions
C) A family of distributions
D) A uniform distribution

Accepted Answer

The chi-square statistic has a family of distributions, known as the chi-square distribution. The specific distribution within this family depends on the degrees of freedom associated with the test.

Question 9

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.

Accepted Answer

The shape of the chi-square distribution is based on the degrees of freedom. A chi-square distribution with a low degree of freedom will be positively skewed, while a chi-square distribution with a high degree of freedom will be less skewed and approach a normal distribution. Choices A, B, and D are incorrect statements.

Question 10

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

Accepted Answer

The chi-square statistic is calculated by summing the squared differences between observed and expected frequencies, therefore resulting in a positive value.

Question 11

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

Accepted Answer

If the null hypothesis is rejected, it indicates that there is a significant association between the two variables in the contingency table, i.e., they are related.

Question 12

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.

Accepted Answer

The goodness-of-fit test is used to test whether the observed frequencies of a categorical variable match the expected frequencies. The variables in this test are based on the nominal measurement scale, which means that they are non-numerical categories or classifications. Therefore, option A is correct. The population distribution does not need to be normal for this test, so option B is incorrect. There is no requirement for all expected frequencies to be equal or unequal, so options C and D are also incorrect.

Question 13

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

Accepted Answer

The chi-square distribution becomes more symmetrical as the degrees of freedom increase. As degrees of freedom increase, the distribution approaches a normal distribution, which is perfectly symmetrical.

Question 14

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

Accepted Answer

The null hypothesis for a goodness-of-fit test is always that there is no preference or difference between the options being compared. Therefore, in this case, the null hypothesis would be that there is no preference between the three new colors proposed for the Jeep Grand Cherokee vehicle.

Question 15

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

Accepted Answer

The answer of For people released from prison, the following...

Question 16

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

Accepted Answer

The number of degrees of freedom for a chi-square goodness-of-fit test is found by k - 1, where k is the number of categories or groups being compared.

Question 17

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) X² D) z-statistic

Accepted Answer

The chi-square (X²) statistic is used to determine how well an observed set of frequencies fits an expected set of frequencies, typically in a chi-square goodness-of-fit test.

Question 18

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

Accepted Answer

The answer of A personnel manager is concerned about absenteeism....

Question 19

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

Accepted Answer

The answer of A personnel manager is concerned about absenteeism....

Question 20

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

Accepted Answer

The null hypothesis in a goodness-of-fit test is rejected if there is a significant difference between the observed and expected frequencies. Therefore, the best choice is B because it states that the difference between the observed and expected frequencies is significantly large. The other choices are incorrect because the computed chi-square value should be greater than the critical value (not less) for the null hypothesis to be rejected, and a small difference between observed and expected frequencies (choice C) would not lead to rejection of the null hypothesis. Choice D is also incorrect because the difference between observed and expected frequencies must not occur by chance to reject the null hypothesis.

Quiz 15: Nonparametric Methods: Nominal Level Hypothesis Tests

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

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 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?

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

The chi-square statistic has __________.

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

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

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

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

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

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 _______________.

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?

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

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

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