studyguidev_part4_solutions_hyptestandreg_

studyguidev_part4_solutions_hyptestandreg_ - Solutions to...

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Solutions to Questions on Hypothesis Testing and Regression 1. A mileage test is conducted for a new car model, the “Pizzazz.” Thirty (n=30) random selected Pizzazzes are driven for a month and the mileage is carefully measured in each. The mean mileage for the sample is 28.6 miles per gallon (mpg) and the sample standard deviation is 2.2 mpg. Estimate a 95% confidence interval for the mean mpg in the entire population of Pizzazzes (you might need to round your answer a little bit to agree with mine). (a) (23.42, 33.84) (b) (27.81, 29.39) (c) (26.82, 30.47) (d) (27.23, 30.03) (e) None of the above 2. Determine the test statistic for testing the null hypothesis that the population mean is 27 mpg ( 0 : 27 : 27 a H H μ = ) (a) t = 3.98 (b) t = -3.98 (c) t = 4.6 (d) t = -4.6 (e) t = 1.96 (f) None of the above 3. A Type II error is made when a. the null hypothesis is accepted when it is false. b. the null hypothesis is rejected when it is true. c. the alternate hypothesis is accepted when it is false. d. the null hypothesis is accepted when it is true. e. the alternate hypothesis is accepted when it is true.
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4. A recent USA TODAY/CNN/Gallup Poll showed that most American people support Bush’s efforts in the Middle East peace process. The poll of 2000 adults was conducted and 1243 people said they supported Bush’s efforts. a) Find a 95% confidence interval for p, the fraction of Americans who support Bush’s efforts phat = 1243/2000 =62.15% then use the CI formula for a proportion b) Perform the hypothesis test Ho : p = 0.6 versus Ha : p > 0.6. - = = = .6215 .60 (.6)(.4)/ 2000 ˆ 62.15% 1.52 p t We reject the null hypothesis if T > 1.64 and since its not, we fail to reject the null hypothesis. 5. A random sample of 100 voters in a community produced 59 voters in favor of candidate A. The observed value of the test statistic for testing the null hypothesis : 0.5 o H p = versus the alternative hypothesis : 0.5 a H p is: a) 1.80 b) 1.90 c) 1.83 d) 1.28 e) 1.75 6. Paul’s housemate Miranda is trying to convince Paul to get a piercing. Paul is very sensitive to popular opinion, however, and will only get one if ”everyone else is doing it”. Of course, everyone is unrealistic, so Paul will settle on getting the piercing if Miranda can show that more than 60% of people at Harvard have one. Miranda wastes no time in taking a sample of 60 people from Adam’s House and performing the appropriate hypothesis test. Her sample revealed 44 people who admitted to having a piercing. (a) Test the hypothesis 0 : 0.6 H p = versus : 0.6 a H p > Will Paul end up getting a piercing ? - = = = = .73 .60 (.6)(.4)/ 60 44 ˆ 73% 60 2.05 p t Since t > 1.64 we reject the null and conclude that more than 60% of students have piercings. (b)
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studyguidev_part4_solutions_hyptestandreg_ - Solutions to...

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