Question

We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20.

The test statistic is:_____
a. 1.50
b. 2.25
c. 1.56
d. .67

Answer 1

H0:
`\sigma^2_1 = \sigma^2_2`

H1:
`\sigma^2_1 \\eq \sigma^2_2`

Now we can calculate the statistic like this:

`F=(s^2_A)/(s^2_B)=(30^2)/(20^2)=2.25`

And the best option would be:

b. 2.25

Explanation:

Information given

`n_A = 25` represent the sample size A

`n_B =16` represent the sample size B

`s_A = 30` represent the sample deviation for A

`s_B = 20` represent the sample deviation for B

Solution to the problem

We want to test if the variation for A it's equal to the variation for B, so the system of hypothesis are:

H0:
`\sigma^2_1 = \sigma^2_2`

H1:
`\sigma^2_1 \\eq \sigma^2_2`

Now we can calculate the statistic like this:

`F=(s^2_A)/(s^2_B)=(30^2)/(20^2)=2.25`

And the best option would be:

b. 2.25