Section 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known 417 Check Your Understanding 7. Which provides stronger evidence against H0: a P-value of 0.05 or a P-value of 0.50? 0.05 8. A test is made of H0 : �� = 30 versus H1: �� < 30. The test statistic is z = −1.28. Find and interpret the P-value. P = 0.1003 9. A test is made of H0 : �� = 6 versus H1: �� ≠ 6. a. The test statistic is z = 0.75. Find and interpret the P-value. P = 0.4532 b. The test statistic is z = −2.20. Find and interpret the P-value. P = 0.0278 c. Which provides stronger evidence against H0 : z = 0.75 or z = −2.20? z = −2.20 Answers are on page 432. The P-value is not the probability that H0 is true Because the P-value is a probability and small P-values indicate that H0 should be rejected, it is tempting to think that the P-value represents the probability that H0 is true. This is not the case. The P-value is the probability that a test statistic such as z would take on an extreme value. Probability is used for events that can be different for different samples. Therefore, it makes sense to talk about the probability that the value of z will be more extreme than an observed value, because the value of z can come out differently for different samples. The null hypothesis, however, is either true or not true. The truth of H0 does not change from sample to sample. For this reason, it does not make sense to talk about the probability that H0 is true. SUMMARY The P-value is the probability, under the assumption that H0 is true, that the test statistic takes on a value as extreme as or more extreme than the value actually observed. The P-value is not the probability that the null hypothesis is true. Check Your Understanding 10. If P = 0.02, which is the best conclusion? ii i. The probability that H0 is true is 0.02. ii. If H0 is true, the probability of obtaining a test statistic more extreme than the one actually observed is 0.02. iii. The probability that H1 is true is 0.02. iv. If H1 is true, the probability of obtaining a test statistic more extreme than the one actually observed is 0.02. Answer is on page 433. Choosing a significance level We have seen that the smaller the P-value, the stronger the evidence against H0. In practice, people often do not choose a significance level. They simply report the P-value and let the reader decide whether the evidence is strong enough to reject H0. Sometimes, however, we need to make a firm decision whether to reject H0. We then choose a significance level �� between 0 and 1 before performing the test, and reject H0 if the P-value is less than or equal to ��. The most commonly used value is �� = 0.05, but other values are sometimes used as well. Next to �� = 0.05, the most commonly used value is �� = 0.01.
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above