Assume that the populations are normally distributed. Test the hypothesis σ1≠σ2 at the α=0.05 level of significance.

Question

Please show the math used to solve the problem. Sorry some people just list answer with none of the math. thanks in advance

Assume that the populations are normally distributed. Test the hypothesis σ1≠σ2 at the α=0.05 level of significance.

(a=0.05)

(Sample1: N = 9 S = 3.7)

(Sample2: N = 9 S = 3.1)

Answer 1

First, square the standard deviations to get the variances:

3.7^2 = 13.69

3.1^2 = 9.61

Next, calculate the F ratio by dividing the first variance by the second

F = 13.69 / 9.61

F = 1.4246

Next, find the critical value of F with the given degrees of freedom at alpha = .05.

The degrees of freedom are n-1 so, 8 (9 -1) and 8 (9 -1)

You will need to look up the critical value in a table or have it calculated online, you don't want to calculate critical values by hand!

In the F table, the critical value at alpha = .05 with 8 and 8 degrees of freedom is 3.44.

The test result is significant if the calculated F is greater than the critical F

In our case, the calculated F, 1.4246, is less than the critical F, 3.44. This means the test is not significant and the SD's are not significantly different.