Question

suppose a researcher is testing the hypothesis $h_0: p = 0.6$ versus $h_1: p < 0.6$ and she finds the $p$-value to be 0.27. explain what this means. would she reject the null hypothesis? why?

a. if the $p$-value for a particular test statistic is 0.27, she expects results no more extreme than the test statistic in about 27 of 100 samples if the null hypothesis is true.

b. if the $p$-value for a particular test statistic is 0.27, she expects results at least as extreme as the test statistic in exactly 27 of 100 samples if the null hypothesis is true.

c. if the $p$-value for a particular test statistic is 0.27, she expects results no more extreme than the test statistic in exactly 27 of 100 samples if the null hypothesis is true.

d. if the $p$-value for a particular test statistic is 0.27, she expects results at least as extreme as the test statistic in about 27 of 100 samples if the null hypothesis is true

choose the correct conclusion below.

a. since this event is not unusual, she will not reject the null hypothesis

b. since this event is unusual, she will reject the null hypothesis

c. since this event is unusual, she will not reject the null hypothesis

d. since this event is not unusual, she will reject the null hypothesis

Explanation:

The P - value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. A P - value of 0.27 means that if the null hypothesis \(H_0:p = 0.6\) is true, we would expect results at least as extreme as the test statistic in about 27 out of 100 samples. In hypothesis testing, we reject the null hypothesis if the P - value is less than the significance level (commonly \(\alpha=0.05\)). Since \(0.27>0.05\), the event (getting a P - value of 0.27) is not unusual (because it is not a small probability event).

Answer:

D. If the P - value for a particular test statistic is 0.27, she expects results at least as extreme as the test statistic in about 27 of 100 samples if the null hypothesis is true.
A. Since this event is not unusual, she will not reject the null hypothesis.