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.

Group of answer choices

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

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

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

Answer 1

using excel add-in phstat>two sample test

we have

F Test for Differences in Two Variances
Data
Level of Significance	0.05
Larger-Variance Sample
Sample Size	5
Sample vaiance	46.8
Smaller-Variance Sample
Sample Size	17
sample varince	13
Intermediate Calculations
F Test Statistic	46.8/13 =3.6
Population 1 Sample Degrees of Freedom	4
Population 2 Sample Degrees of Freedom	16
Two-Tail Test
Upper Critical Value	3.729417
p-Value	0.056401
Do not reject the null hypothesis

since p-value is greater than 0.05 so do not reject Ho . So

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