Question 1

The chi-square distribution is ________.

Accepted Answer

The chi-square distribution is positively skewed, meaning that its tail is longer on the right-hand side. This is because the values of the chi-square variable are always positive.

Question 2

The contingency table for a sample of corporate executives classified by educational level and social activity follows.  What does the expected frequency for the "Above Average" social activity and "High School" education equal?

Accepted Answer

The answer of The contingency table for a sample of...

Question 3

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?

Accepted Answer

To conduct a goodness-of-fit test, we use the chi-square distribution. The critical value of chi-square with four degrees of freedom at the 0.01 level of significance is 13.277.

We can look up the critical value in a chi-square distribution table or use a calculator or software. Therefore, the best choice is (C).

Question 4

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?

Accepted Answer

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

Question 5

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

Accepted Answer

In this case, the computed chi-square value (6.079) is less than the critical value (9.488). Therefore, we fail to reject the null hypothesis, which means that there is no significant difference between the observed and expected frequencies. The difference is likely due to random sampling error.

Question 6

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

Accepted Answer

A contingency table analysis is the appropriate test for determining if two nominal variables are related. It allows us to compare observed frequencies to expected frequencies and determine if there is a significant association between the variables. The other options (goodness-of-fit, ANOVA table, and regression analysis) are not appropriate for testing the relationship between two nominal variables.

Question 7

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

Accepted Answer

This two-way classification is called a contingency table as it shows the contingency or dependence between the two variables, gender and college attended. It displays the frequency distribution of each combination of categories for the two variables.

Question 8

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

Accepted Answer

The null hypothesis for a goodness-of-fit test is that there is no preference between the colors, which fits option B. Options A and C suggest a preference for a specific color, which does not fit the null hypothesis. Option D suggests that the test cannot be conducted at all, which is not a valid option.

Question 9

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

Accepted Answer

A goodness-of-fit test is used to test whether an observed frequency distribution fits a theoretical distribution. It can be applied when the data are measured with a nominal or ordinal scale. The assumptions for this test do not require the population to be normally distributed or for the population variance or mean to be known.

Question 10

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

Accepted Answer

The degrees of freedom for a contingency table analysis is calculated by multiplying the number of rows minus one by the number of columns minus one i.e. (Rows - 1) x (Columns - 1). This gives the total number of cells in the contingency table that are free to vary, while taking into account the constraints imposed by the row and column totals.

Question 11

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?

Accepted Answer

The critical value for a contingency table with 3 rows and 3 columns (as in this case) at the 0.01 level of significance is 11.345, according to a chi-square distribution table. Therefore, the best choice is C.

Question 12

The chi-square statistic has ________.

Accepted Answer

The chi-square statistic follows a family of distributions known as the chi-square distribution. The specific distribution within this family depends on the degrees of freedom (df) associated with the statistic. Therefore, the answer is C - a family of distributions.

Question 13

The chi-square statistic ________.

Accepted Answer

The chi-square statistic is always greater than or equal to zero. It cannot be negative or equal to zero.

Question 14

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

Accepted Answer

The goodness-of-fit test is used to determine whether an observed frequency distribution fits a theoretical distribution. Variables in this test are based on the nominal measurement scale, which allows us to categorize data into distinct groups. The other options are incorrect as a normal population is not required for this test, and expected frequencies may be equal or unequal depending on the theoretical distribution being tested.

Question 15

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

Accepted Answer

The chi-square distribution becomes more symmetrical as the degrees of freedom increase. As the sample size increases, the expected frequencies in each category become larger, and the sampling distribution more closely approximates the normal distribution.

Question 16

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

Accepted Answer

If the null hypothesis is rejected in a chi-square test involving a contingency table, it means that there is a significant association between the two variables being studied. In other words, they are related. Therefore, the correct answer is D.

Question 17

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?

Accepted Answer

The computed chi-square value of 1.273 is much smaller than the critical value of 13.388, indicating that there is not enough evidence to reject the null hypothesis. Therefore, we can conclude that the goodness-of-fit test does not show significant deviation between the observed and expected frequencies.

Question 18

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

Accepted Answer

The number of degrees of freedom for a chi-square goodness-of-fit test is equal to the number of categories minus one, so the formula is k - 1.

Question 19

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

Accepted Answer

The shape of the chi-square distribution is based on the degrees of freedom. The distribution is positively skewed and the variance of the distribution depends on the degrees of freedom as well. Option A is incorrect as the distribution is positively skewed. Option B is incorrect as the numerator and denominator degrees of freedom are not two separate sets but are linked. Option D is incorrect as the variance of the distribution is dependent on the degrees of freedom.

Question 20

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

Accepted Answer

As the degrees of freedom increase, the chi-square distribution becomes more symmetric and starts to resemble a normal distribution more closely. Among the given options, the distribution with 15 degrees of freedom would be closest to a normal distribution.

Quiz 15: Nonparametric Methods: Nominal Level Hypothesis Tests