Question

Comparing two population means and not knowing the population standard deviation I would use which distribution?

	A.	Two Sample Z statistic, equation 11-2
	B.	Two Sample t statistic, equation 11-4, assuming equal variances
	C.	Two Sample t statistic, equation 11-5, assuming unequal variances
	D.	either B or C

Answer 1

For comparing the differences between two population means for which the population standard deviation is unknown, hypothesis test is conducted for comparing the difference between sample means of the two populations. This hypothesis test is used for finding a confidence interval for the difference between the two population means () using the sampling distribution for the difference between the sample means (). The samples are taken independently and the standard deviation is calculated as:

Here, when population standard deviations and are unknown, they have to be estimated by the two sample sizes, s₁ and s₂, respectively.

In this case, there are two ways for estimating the two variances ( and ) for the t-test of 2 independent samples:

a. t-test of 2 independent samples assuming they have pooled or equal variance, and
b. t-test of 2 independent samples assuming they have separate or unequal variance

The t-test with pooled or equal variances is used when the two populations have almost equal variances, else, t-test with separate or unequal variances is used.

Therefore, option D is the answer.