Critical Thinking: One-Tailed versus Two-Tailed Tests (a) For the same data and null hypothesis, is...

Critical Thinking: One-Tailed versus Two-Tailed Tests

(a) For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.

(b) For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject H_{0} while a two-tailed test results in the conclusion to fail to reject H_{0}? Explain.

(c) For the same data, null hypothesis, and level of significance, if the conclusion is to reject H_{0} based on a two-tailed test, do you also reject H_{0} based on a one-tailed test? Explain.

(d) If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain.