Chapter Quiz 469 Section 9.5: When a population is almost exactly normal, we can test a hypothesis about a population standard deviation. We use the chi-square distribution, with degrees of freedom 1 less than the sample size. Section 9.6: We have learned to perform hypothesis tests for a population mean, a population proportion, and a population standard deviation or variance. There are two tests for a population mean, the z-test and the t-test. The test to use depends on whether the population standard deviation �� is known. Section 9.7: The power of a test is the probability that a false H0 is rejected. It is desirable for a test to have a high degree of power. If the sample size remains the same, however, increasing the power also increases the probability of a Type I error. In order to increase the power without increasing the probability of a Type I error, it is necessary to increase the sample size. Vocabulary and Notation alternate hypothesis 404 one-tailed hypothesis 405 statistically significant 411 critical region 410 P-value 415 t-test 433 critical value 410 P-value method 414 test statistic 410 critical value method 409 power 464 two-tailed hypothesis 405 hypothesis test 406 rejecting H0 406 Type I error 407 left-tailed hypothesis 405 right-tailed hypothesis 405 Type II error 407 null hypothesis 404 significance level 411 Important Formulas Test statistic for a mean, standard deviation known: Test statistic for a proportion: z = ̄x − ��0 ��∕ √ n z = ̂p − p0 √ p0(1 − p0) n Test statistic for a mean, standard deviation unknown: Test statistic for a standard deviation: t = ̄x − ��0 √ n s∕ ��2 = (n − 1) ⋅ s2 ��2 0 Chapter Quiz 1. Fill in the blank: A test of the hypotheses H0 : �� = 65 versus H1: �� ≠ 65 was performed. The P-value was 0.035. Fill in the blank: If �� = 65, then the probability of observing a test statistic as extreme as or more extreme than the one actually observed is . 0.035 2. A hypothesis test results in a P-value of 0.008. Which is the best conclusion? iv i. H0 is definitely false. ii. H0 is definitely true. iii. H0 is plausible. iv. H0 might be true, but it’s very unlikely. v. H0 might be false, but it’s very unlikely. 3. True or false: If P = 0.03, then a. The result is statistically significant at the �� = 0.05 level. True b. The result is statistically significant at the �� = 0.01 level. False c. The null hypothesis is rejected at the �� = 0.05 level. True d. The null hypothesis is rejected at the �� = 0.01 level. False 4. A null hypothesis is rejected at the �� = 0.05 level. True or false: a. The P-value is greater than 0.05. False b. The P-value is less than or equal to 0.05. True c. The result is statistically significant at the �� = 0.05 level. True d. The result is statistically significant at the �� = 0.10 level. True 5. A sample of size 8 is drawn from a normal population with mean ��, and the population standard deviation is unknown. a. Is it appropriate to perform a z-test? Explain. No b. Is it appropriate to perform a t-test? Explain. Yes 6. A test will be made of H0 : �� = 4 versus H1: �� > 4, using a sample of size 25. The population standard deviation is unknown. Find the critical value of the test statistic if the significance level is �� = 0.05. 1.711 7. True or false: We never conclude that H0 is true. True
navidi_monk_elementary_statistics_2e_ch7-9
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