Question

A large department store examined a sample of 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa, and Discover. Six MasterCard sales, seven Visa, and five Discover sales were recorded. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic?

Answer 1

In a one-way ANOVA test with three groups and 18 total observations, the degrees of freedom for the F statistic are 2 for the numerator (number of groups minus one) and 15 for the denominator (number of observations minus number of groups).

Step-by-step explanation:

The question involves determining the degrees of freedom for the F statistic in a one-way ANOVA test. The F statistic compares the variance within each group to the variance between the group means.

There are two types of degrees of freedom in an ANOVA test: the numerator degrees of freedom and the denominator degrees of freedom. The numerator degrees of freedom is equal to the number of groups minus one. In this case, since there are three types of credit cards (MasterCard, Visa, and Discover), we have 3 - 1 = 2.

The denominator degrees of freedom is equal to the total number of observations minus the number of groups. With 18 credit card sales and three groups, the denominator degrees of freedom is 18 - 3 = 15.

Therefore, the degrees of freedom for the F statistic in this ANOVA test are 2 for the numerator and 15 for the denominator.

Answer 2

2 in the numerator, 15 in the denominator

Step-by-step explanation:

Since there are three types of credit cards, the degree of freedom for numerator is 3-1 = 2.

Since there are 18 credit card sales, the degree of freedom for denominator is

18-3 = 15

So answer is 2 in the numerator, 15 in the denominator