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Chapter 8: Q. 9.54 (page 370)
Which provides stronger evidence against the null hypothesis, a P-value of or a P-value of ?Explain your answer.
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P-Values. In Exercises 17–20, do the following:
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value. (See Figure 8-3 on page 364.)
c. Using a significance level of = 0.05, should we reject or should we fail to reject ?
The test statistic of z = -1.94 is obtained when testing the claim that .
Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Lie Detectors Trials in an experiment with a polygraph yield 98 results that include 24 cases of wrong results and 74 cases of correct results (based on data from experiments conducted by researchers Charles R. Honts of Boise State University and Gordon H. Barland of the Department of Defense Polygraph Institute). Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. Based on the results, should polygraph test results be prohibited as evidence in trials?
Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.
Airport Data Speeds: The claim that for Verizon data speeds at airports, the mean. The sample size is and the test statistic is
t =-1.625 .
PowerFor a hypothesis test with a specified significance level , the probability of a type I error is, whereas the probability of a type II error depends on the particular value ofpthat is used as an alternative to the null hypothesis.
a.Using an alternative hypothesis ofp< 0.4, using a sample size ofn= 50, and assumingthat the true value ofpis 0.25, find the power of the test. See Exercise 34 “Calculating Power”in Section 8-1. [Hint:Use the valuesp= 0.25 andpq/n= (0.25)(0.75)/50.]
b.Find the value of , the probability of making a type II error.
c.Given the conditions cited in part (a), find the power of the test. What does the power tell us about the effectiveness of the test?
Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Drug Screening The company Drug Test Success provides a “1-Panel-THC” test for marijuana usage. Among 300 tested subjects, results from 27 subjects were wrong (either a false positive or a false negative). Use a 0.05 significance level to test the claim that less than 10% of the test results are wrong. Does the test appear to be good for most purposes?
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