Alarge 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?

a. 3 in the numerator, 18 in the denominator

b. 18 in the numerator, 3 in the denominator

c. 6 in the numerator, 15 in the denominator

d. 2 in the numerator, 15 in the denominator

d. 2 in the numerator, 15 in the denominator

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have groups and on each group from we have individuals on each group we can define the following formulas of variation:  

We want to test this hypothesis:

And we have this property  

The degrees of freedom for the numerator on this case is given by where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by .

And the total degrees of freedom would be

On this case the correct answer would be 2 for the numerator and 15 for the denominator.  

d. 2 in the numerator, 15 in the denominator

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.