Question

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population with the following results:

Sample 1	Sample 2
Sample Mean = 5275	Sample Mean = 5240
s1 = 150	s2 = 200

To test the null hypothesis H₀: µ₁ - µ₂ = 0 versus the alternative hypothesis H_a: µ₁ - µ₂ ╪ 0 versus the alternative hypothesis at the 0.05 level of significance, the most accurate statement is

The value of the test statistic is 2.80 and the critical values are +1.645 and -1.645

The value of the test statistic is 2.80 and the critical values are +1.96 and -1.96

The value of the test statistic is 3.29 and the critical value is +1.645

The value of the test statistic is 3.29 and the critical values are +1.645 and -1.645

The value of the test statistic is 2.80 and the critical value is +1.96

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.
Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 400 + 400 - 2 = 798
For . Since , we reject the null hypothesis H0 in favor of the alternative hypothesis .

The value of the test statistic is 2.80 and the critical values are +1.96 and -1.96