8-3 Testing a Claim About a Mean 413 Statistical Literacy and Critical Thinking 1.Basketball Player Salaries Listed below are salaries (millions of dollars) of professional basketball players in a recent year. What requirements must be satisfied to test the claim that the salaries are from a population with a mean greater than 5 million dollars? Are those requirements satisfied? 11222222446791236 2. df If we are using the sample data from Exercise 1 for a t test of the claim that the population mean is greater than $5 million, what does df denote, and what is its value? 3. t Test Exercise 2 refers to a t test. What is a t test? Why is the letter t used? What is unrealistic about the z test method described at the end of this section? 4.Test Statistic and Critical Value The statistics for the sample data in Exercise 1 are n = 15, x = 6.133333, and s = 8.862978, where the units are millions of dollars. Find the test statistic and critical value(s) for a test of the claim that the salaries are from a population with a mean greater than 5 million dollars. Assume that a 0.05 significance level is used. 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. Based on the result, what is the final conclusion? 5.Weights of Quarters The claim is that weights (grams) of quarters made after 1964 have a mean equal to 5.670 g as required by mint specifications. The sample size is n = 40 and the test statistic is t = -3.135. 6. Weights of Pennies The claim is that weights (grams) of pennies made after 1983 have a mean equal to 2.500 g as required by mint specifications. The sample size is n = 37 and the test statistic is t = -0.331. 7.Cotinine in Smokers The claim is that smokers have a mean cotinine level greater than the level of 2.84ng>mL found for nonsmokers. (Cotinine is used as a biomarker for exposure to nicotine.) The sample size is n = 902 and the test statistic is t = 56.319. 8.Body Temperatures The claim is that for 8 AM body temperatures of males, the mean is less than 98.6°F. The sample size is n = 33 and the test statistic is t = -4.411. 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. 9.Peanut Butter Cups Data Set 38 “Candies” includes weights of Reese’s peanut butter cups. The accompanying Statdisk display results from using all 38 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. 10.Taxi Times Data Set 32 “Taxis” in Appendix B includes times (minutes) of taxi cab rides in New York City. Using the first 36 times to test the claim that the mean of all such times is less than 15 minutes, the accompanying Minitab display is obtained. 11. Tower of Terror Data Set 33 “Disney World Wait Times” includes wait times (minutes) for the Tower of Terror ride at 5:00 PM. Using the first 40 times to test the claim that the mean of all such wait times is more than 30 minutes, the accompanying Excel display is obtained. 8-3 Basic Skills and Concepts Statdisk Minitab Excel (XLSTAT)
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