Question

Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76

Answer 1

The critical values of F at 95% confidence are 0.359 and 2.788.

Explanation:

We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:

Store A Store B

nA = 21 nB = 16

SA = 28.284 SB = 20

And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.

AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.

The test statistics for F-test is =
`(S_A^(2) )/(S_B^(2) ) * (\sigma_B^(2) )/(\sigma_A^(2) )` ~
`F__n_A_-_1,_ n_B_-_1`

where,
`S_A` and
`S_B` are sample standard deviations.

Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;

2.788 for right-part and 0.359 for the left-part.