Question

Researchers were interested whether students self-identifying as conservative or liberal at a local community college differed on Grade Point Average (GPA). The sample data were entered into a statistical software program, and the output for the F test is shown below. To compare the two means, would it be appropriate to use a t test that assumes equal variances?

F-Test Two-Sample for Variances
		Conservative	Liberal
	Mean	3.156	3.182
	Variance	0.26	0.24
	Observations	45	113
	df	44	112
	F	1.0827
	P(F<=f) one-tail	0.3620
	F Critical one-tail	1.485

A.        Yes, because the sample statistics (the F test) show that the variances are equal at α = .05.

B.        No, because the sample statistics (the F test) show that the variances are unequal at α =    .05.

C.        No, because a z test should be used instead of a t test.

D.        No, because the F test is not the proper test to compare two variances.

Answer 1

We know that For testing Two-Sample for Variance F-Test is appropriate. Here our null hypothesis is variance are equal for both the population

And here from the output we see that the test is one tailed test.

Rejection Rule:

We reject the null hypothesis if Observed F> F Critical One tail

Here from the output we get , Observed F= 1.0827 and F Critical One tail = 1.485

So we get Observed F= 1.0827 < F Critical One tail = 1.485

Result: Do not reject null hypothesis. i.e. Population variance are equal at level

Now we want to compare the two population means. We know that for testing 2-sample population mean our appropriate test statistic is given by,

[ under ]

Where, Sample Mean of 1st sample ,   Sample Mean of 2nd sample ,

Number of observation for 1st sample ,   Number of observation for 2nd sample ,

Sample Standard Deviation for 1st sample ,       Sample Standard Deviation for 2nd sample ,

and we also assume equality of population variance.

i.e. compare the two population means 2-sample t test with assume equal variances is appropriate.

Answer: Correct answer is " Option A. (Yes, because the sample statistics (the F test) show that the variances are equal at α = .05) "

[ Note :Z test is used when population SD is known and  F test is the proper test to compare two variances.]