Question

A researcher is trying to decide if the homogeneity of variance assumption is met before conducting an independent samples t test. Sample 1: df = 4, s2 = 46.8 Sample 2: df = 16, s2 = 13

The researcher performs an F test in order to decide which version of the t test (pooled or unpooled) to use and whether to correct degrees of freedom for the t test. Perform the test and pick which alternative the researcher should use. Assume alpha equals 0.05.

A. Use unpooled variance to calculate the t test and use corrected df to get a more stringent t critical.

B. Use pooled or unpooled variance, because both versions of the t test will produce exactly the same t ratio.

C. Use pooled variance and calculate degrees of freedom for the t test normally.

Answer 1

Here we have given that,

Degrees of freedom of sample 1= 4

= sample variance of sample 1= 46.8

Degrees of freedom of sample 2= 16

= sample variance of sample 2= 13

Now, we need to perform F-test to check for the version t-test we need to use (Pooled or unpooled)

No, we can check the homogeneity of variance assumption using the test of two population variance (F-test).

Claim: To check whether the two population variance equal or not.

The null and alternative hypothesis is as follows,

Versus

The test statistics is as follows,

=

   =3.60

The test statistics is 3.60.

Now, we can find the p-value,   

p-value = 0.0282 Using EXCEL software = FDIST(F-statistics= 3.60, Degrees of freedom of sample 1= 4,Degrees of freedom of sample 2= 16)

The p-value is 0.0282

Decision:

=level of significance=0.05

Here, P-value (0.0282) less than (<) (0.05)

We reject the Null hypothesis Ho. we can conclude that the two opulation variances are not equal.

In General, we know that if the homogeneity of variance assumptions satisfies we can use the pooled variance approach otherwise we can use the unpolled variance approach to perform t-test.

i.e. here option A is correct.

Use unpooled variance to calculate the t test and use corrected df to get a more stringent t critical.