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 larger 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 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. 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. 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. (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. Yes. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α. No. If the two-tailed P-value is smaller than α, the one-tailed area will be larger than α. 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 is also smaller 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. Yes. The conclusions can be different. Yes. The conclusions will be the same. No. The conclusions will be the same. No. The conclusions can be different.

Answer 1

Sol:

(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.

If you Satisfy with Answer, Please give me "Thumb Up". It was very important to me.