Question

Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that variances of two populations are not the same (σ21≠ σ22). At a level of significance of α = 0.01, when should you reject H0? n1 = 25 n2 = 30 x1 = 27 x2 = 25 s1 = 1.5 s2 = 1.9

		Reject H0 if the standardized test statistic is less than -2.787 or greater than 2.787.
		Reject H0 if the standardized test statistic is less than -2.797 or greater than 2.797.
		Reject H0 if the standardized test statistic is less than -1.711 or greater than 1.711.
		Reject H0 if the standardized test statistic is less than -2.492 or greater than 2.492.

Answer 1

We have to test

Given that :

Assume that variances of two populations are not the same .

So we need to use two sample t-test unpooled ( not pooled).

Test statistic formula is,

Therefore standardized test statistic is 4.361

Now to find critical value for level of significance

Degrees of freedom is smallest of

25-1 = 24

30-1 = 29

Therefore degrees of freedom= 24

Using Excel function , =TINV (alpha,DF)

= TINV (0.01,24)

As this is two tailed test critical values are -2.797 and 2.797

Decision rule :

If standardized tests statistic is less than -t critical value or greater than +t critical value.

We Reject Ho ,as standardized test statistic (4.361) is greater than t critical value (2.797)

Therefore the correct choice is

Reject H0 if the standardized test statistic is less than -2.797 or greater than 2.797.