Question

Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 3.9288. 6.2597 is the standard deviation of the second sample.

Answer 1

2.539

Explanation:

Standard deviation of sample 1 = 3.9288

Standard deviation of sample 1 = 6.2597(

Standard deviation = √variance

Variance = (standard deviation)^2

Variance of sample 1 = (3.9288)^2 = 15.43546944

Variance of sample 2 = (6.2597)^2 = 39.18384409

For two samples:

F stat = (variance 1) / (variance 2)

Since the variance of sample is large, we place it in th e numerator

F stat = (39.18384409) / (15.43546944)

F stat = 2.5385586

F stat = 2.539

Answer 2

F test = 2.54

Explanation:

We are given two samples

Standard deviation of the first sample = 3.9288

Standard deviation of the second sample = 6.2597

F test statistic = Variance of the Larger sample/ Variance of the smaller sample

Variance = (Standard deviation)²

Variance for the first sample = 3.9288²

= 15.43546944

Variance for the second sample = 6.2597² = 39.18384409

F test = 39.18384409/15.43546944

= 2.5385586258

Therefore, the F test approximately = 2.54