Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using a = 0.05. One student used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null hypothesis. Which of these might have been their calculated value of t?
A) 1.88
B) 2.66
C) 1.55
D) 2.22
E) 1.22

Question

Quizplus · Accepted Answer

Since one student used a one-tail test and rejected the null hypothesis, they were looking for evidence that one population mean was significantly larger than the other. The critical value for a one-tail test with a significance level of 0.05 and degrees of freedom in the thousands (as is likely with very large samples) is around 1.645. Therefore, a calculated t-value of 1.88 could lead to rejecting the null hypothesis in favor of the alternative hypothesis that one population mean is significantly larger than the other.

The other student used a two-tail test and failed to reject the null hypothesis, meaning they were looking for evidence that the two population means were significantly different from each other. The critical value for a two-tail test with a significance level of 0.05 and degrees of freedom in the thousands is around 1.96. A calculated t-value of 1.88 would not lead to rejecting the null hypothesis in this case.

Based on Data from Two Very Large Independent Samples, Two