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. Which of these might have been their calculated value of t?
A) 1.25
B) 2.25
C) 1.75
D) 1.50
E) 2.50

Question

Quizplus · Accepted Answer

The calculated value of t that would allow one student to reject the null hypothesis using a one-tail test but not using a two-tail test at the same significance level (α = 0.05) is likely to be a value that is significant in a one-tail test but not in a two-tail test. This typically occurs with a t-value that is between the critical values for a one-tail and a two-tail test at the same α level. A t-value of 1.75 is plausible for this scenario, as it might be significant in a one-tail test (where the critical value could be around 1.645 for α = 0.05) but not in a two-tail test (where the critical value would be higher, around 1.96 for α = 0.05).

Based on Data from Two Very Large Independent Samples, Two