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Chapter 8: Q. 9.6 (page 357)
Suppose that, in a hypothesis test, the null hypothesis is in fact true.
a. Is it possible to make a Type I error? Explain your answer.
b. Is it possible to make a Type II error? Explain your answer.
Part (a). Yes
Part (b). No
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A formal hypothesis test is to be conducted using the claim that the mean height of men is equal to 174.1 cm.
a. What is the null hypothesis, and how is it denoted?
b. What is the alternative hypothesis, and how is it denoted?
c. What are the possible conclusions that can be made about the null hypothesis?
d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm”?
Video Games: Checking Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from “content and rating of Teen-Rated Video Games,” by Haninger and Thompson, journal of the American Medical Association, Vol.291, No.7). What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 sec? Are the requirements all satisfied?
84 14 583 50 0 57 207 43 178 0 2 57
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?
Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.
a. Find the critical value(s).
b. Using a significance level of = 0.05, should we reject or should we fail to reject ?
Exercise 18
Technology. In Exercises 9–12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Airport Data Speeds Data Set 32 “Airport Data Speeds” in Appendix B includes Sprint data speeds (mbps). The accompanying TI-83/84 Plus display results from using those data to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results.
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