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Chapter 8: Q. 9.10 (page 357)
Answer true or false and explain your answer: For a fixed sample size, decreasing the significance level of a hypothesis test results in an increase in the probability of making a Type II error.
True.
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Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. 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.
Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
69 81 39 65 42 21 60 63 66 48 64 70 96 91 65
In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Null and Alternative Hypotheses Identify the null hypothesis and alternative hypothesis.
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.
Tennis Instant Replay The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by referees. In a recent U.S. Open, singles players made 879 challenges and 231 of them were successful, with the call overturned. Use a 0.01 significance level to test the claim that fewer than 1/ 3 of the challenges are successful. What do the results suggest about the ability of players to see calls better than referees?
Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.
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
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