Question

Consider the following.

(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 your answer.

The P-value for a one-tailed test is smaller because the two-tailed test includes the area in only one tail.The P-value for a one-tailed test is smaller because the two-tailed test includes the area in both tails.     The P-value for a one-tailed test is larger because the two-tailed test includes the area in only one tail.The P-value for a one-tailed test is larger because the two-tailed test includes the area in both tails.

(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 H₀ while a two-tailed test results in the conclusion to fail to reject H₀? Explain your answer.

Yes. The P-value for a one-tailed test might be smaller than α, while the P-value for a two-tailed test could be larger than α.No. The P-value for a one-tailed test might be smaller than α, while the P-value for a two-tailed test could be larger than α.     Yes. When the P-value for a one-tailed test is smaller than α, the P-value for a two-tailed test will also be smaller than α.No. When the P-value for a one-tailed test is smaller than α, the P-value for a two-tailed test will also be smaller than α.

(c) For the same data, null hypothesis, and level of significance, if the conclusion is to reject H₀ based on a two-tailed test, do you also reject H₀ based on a one-tailed test? Explain your answer.

No. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α.Yes. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α.     Yes. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α.No. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α.

(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 your answer.

No. The conclusions can be different.No. The conclusions will be the same.     Yes. The conclusions will be the same.Yes. The conclusions can be different.

Answer 1

(a)

P-value of two-tailed test is twice the p-value of one-tailed test.

The P-value for a one-tailed test is smaller because the two-tailed test includes the area in both tails.

(b)

P-value of two-tailed test is twice the p-value of one-tailed test. So it is possible that that p-value of one tail test will be smaller than α, but the p-value of two-tail test be larger than α.

Yes. The P-value for a one-tailed test might be smaller than α, while the P-value for a two-tailed test could be larger than α.

(c)

P-value of two-tailed test is twice the p-value of one-tailed test. So if p-value of two tail test is smaller than α, then the p-value of one-tail test will be smaller than α.

Yes. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α.

(d)

Yes. The conclusions can be different.

Because the alternative hypothesis of one-tail test and two-tail test differ so, conclusions after rejecting the null hypothesis would differ.