Question

Use the given information to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom. F = 4.23, df1 = 4, df2 = 5 p-value < 0.005 0.005 < p-value < 0.010 0.010 < p-value < 0.025 0.025 < p-value < 0.050 0.050 < p-value < 0.100 p-value > 0.100

Answer 1

The range of the p-value is: 0.050 < p-value < 0.100.

Explanation:

For checking the equivalence of two population variances of independent samples, we use the f-test.

The test statistic is given by:

`F=(S_(1)^(2))/(S_(2)^(2))\sim F_{\alpha, (n_(1)-1)(n_(2)-1)}`

It is provided that the hypothesis test is one-tailed.

The computed value of the test statistic is:

F = 4.23.

The degrees of freedom of the numerator and denominator are:

`df_(1)=4\\df_(2)=5`

Use MS-Excel to compute the p-value as follows:

Step 1: Select function fX → F.DIST.RT.

Step 2: A dialog box will open. Enter the values of f-statistic and the two degrees of freedom.

*See the attachment below.

Step 3: Press OK.

The p-value is, 0.0728.

The range of the p-value is:

0.050 < p-value < 0.100