10 Review Exercises 572 CHAPTER 10 Chi-Square Tests and the F-Distribution Section 10.1 In Exercises 1–4, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the chi-square test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 1. A researcher claims that the age distribution of U.S. physicians is different from the distribution shown in the pie chart. You randomly select 400 U.S. physicians and ask them their age. The table shows the results. At a = 0.01, test the researcher’s claim. (Adapted from Medscape) less than 40 20% 40–49 50–59 26% 28% 60–69 22% 70 and older 4% Survey results Age Frequency, f Less than 40 100 40–49 85 50–59 125 60–69 70 70 and older 20 2. A researcher claims that the distribution of the amounts that parents give their children per week for an allowance is different from the distribution shown in the pie chart. You randomly select 1509 parents and ask them how much they give their children per week for an allowance. The table shows the results. At a = 0.10, test the researcher’s claim. (Adapted from T. Rowe Price) Survey results Response Frequency, f $5 or less 220 $6–$10 312 $11–$20 539 $21–$50 337 $51 or more 101 3. A sports website claims that the opinions of golfers about what irritates them the most on the golf course are distributed as shown in the pie chart. You randomly select 1018 golfers and ask them what irritates them the most on the golf course. The table shows the results. At a = 0.05, test the sports website’s claim. (Adapted from GOLF.com) Survey results Response Frequency, f Slow play 646 Poor course conditions 201 Poor etiquette 126 High green fees 45 $5 or less 14% $51 or more 7% $21 to $50 22% $6 to $10 22% $11 to $20 35% FIGURE FOR EXERCISE 2 Poor course conditions 18.5% High green fees 5.3% Poor etiquette 11.1% Slow play 65.1% FIGURE FOR EXERCISE 3
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