In testing the difference between two population means using two independent samples, the population standard deviations were assumed to be known and the calculated test statistic equalled 2.56. If the test was two-tailed and a 5% level of significance had been specified, what would be the most appropriate conclusion from the findings?
A) to reject the null hypothesis
B) not to not reject the null hypothesis
C) to choose two other independent samples
D) to accept the null hypothesis

Question

Quizplus · Accepted Answer

To determine whether to reject or not reject the null hypothesis, we need to compare the calculated test statistic with the critical value from the t-distribution at a 5% level of significance with degrees of freedom calculated based on the sample sizes.
Since this is a two-tailed test, we need to consider both tails of the distribution. At a 5% level of significance, the critical values for this test with degrees of freedom equal to the smaller of the two sample sizes minus 1 is approximately +/- 2.571. Since the calculated test statistic of 2.56 falls inside the range of +/- 2.571, we can reject the null hypothesis and conclude that there is a significant difference between the two population means.

In Testing the Difference Between Two Population Means Using Two