Section 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known 425 Check Your Understanding 19. A hypothesis test is performed at a significance level �� = 0.05. What is the probability of a Type I error? 0.05 20. Charlie will perform a hypothesis test at the �� = 0.05 level. Felice will perform the same test at the �� = 0.01 level. a. If H0 is true, who has a greater probability of making a Type I error? Charlie b. If H0 is false, who has a greater probability of making a Type II error? Felice Answers are on page 433. Objective 5 Report the P-value or the test statistic value Report the P-Value or the Test Statistic Value Sometimes people report only that a test result was statistically significant at a certain level, without giving the P-value. It is common, for example, to read that a result was ‘‘statistically significant at the 0.05 level’’ or ‘‘statistically significant (P ≤ 0.05).’’ It is much better to report the P-value along with the decision whether to reject. There are two reasons for this. The first reason is that there is a big difference between a P-value that is just barely small enough to reject, say P = 0.049, and a P-value that is extremely small, say P = 0.0001. If P = 0.049, the evidence is just barely strong enough to reject H0 at the �� = 0.05 level, whereas if P = 0.0001, the evidence against H0 is overwhelming. Thus, reporting the P-value describes exactly how strong the evidence against H0 is. The second reason is that not everyone may agree with your choice of ��. For example, let’s say you have chosen a significance level of �� = 0.05. You obtain a P-value of P = 0.03. Since P < 0.05, you reject H0. Let’s say that you report only that H0 is rejected at the �� = 0.05 level, without stating the P-value. Now imagine that the person reading your report believes that a Type I error would be very serious, so that a significance level of �� = 0.01 would be more appropriate. This reader cannot tell whether to reject H0 at the �� = 0.01 level, because you have not reported the P-value. It is much more helpful to report that P = 0.03, so that people can decide for themselves whether or not to reject H0. When using the critical value method, you should report the value of the test statistic, rather than simply stating whether the test statistic was in the critical region. In this way, the reader can tell whether the value of the test statistic was just barely inside the critical region, or well inside. In addition, reporting the value of the test statistic gives the reader the opportunity to choose a different critical value and determine whether H0 can be rejected at a different level. SUMMARY When presenting the results of a hypothesis test, state the P-value or the value of the test statistic. Don’t just state whether or not H0 was rejected. Check Your Understanding 21. A test was made of the hypotheses H0 : �� = 15 versus H1: �� > 15. Four statisticians wrote summaries of the results. For each summary, state whether it contains enough information. If there is not enough information, indicate what needs to be added. a. The P-value was 0.02, so we reject H0 at the �� = 0.05 level. Enough information b. The critical value was 1.645. Because z > 1.645, we reject H0 at the �� = 0.05 level. State value of test statistic c. The critical value was 1.645. Because z = 2.05, we reject H0 at the �� = 0.05 level. Enough information d. Because P < 0.05, we reject H0 at the �� = 0.05 level. State P-value Answers are on page 433.
navidi_monk_elementary_statistics_2e_ch7-9
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