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STATS Homework Assignment 2 Problems




Question;Question 1: (10 points)Suppose 400 randomly selected alumni from Miami University were asked to rate theuniversitys counseling services on a 1 to 10 scale. The sample mean was found to be 8.6.Assume the population standard deviation is known to be 2.0.a. John Smith computes the 95% confidence interval for the average satisfaction score as8.6 1.96(2). What is his mistake?b. After correcting his mistake in part (a), he states I am 95% confident that the samplemean falls between 8.404 and 8.796. What is wrong with his statement?c. Finally, in his defense of using the Normal Distribution to determine the confidencecoefficient he says, Because the sample size is quite large, the population of alumnirating will be approximately Normal. Explain to John his misunderstanding and correcthis statementQuestion 2: (10 points)The mean score for all U.S. high school seniors taking the SAT college entrance exam equals500. A study is conducted to see whether a different mean applies to Canadian seniors. For arandom sample of 100 Canadian seniors, suppose the mean and standard deviation on thisexam equal 508 and 100.a. Set up hypotheses for a significance test, and compute the test statistic.b. The P-value is 0.43. Interpret it, and make a decision about H0, using a significance levelof 0.05.c. If the decision in (b) was in error, what type of error is it?Question 3 (10 points)A nationwide study of American homeowners revealed that 65% have one or more lawnmowers. A lawn equipment manufacturer located in Omaha, feels the estimate is too low forhouseholds in Omaha and predicts this amount to be higher. Can the value 0.65 be rejected if asurvey of 490 homes in Omaha yields 336 with one or more lawn mowers? Use = 0.05. (Showall steps)Question 4: (10 points)The ages (in years) at first transplant for a sample of 11 heart transplant patients are as follows:54 42 51 54 49 56 33 58 54 64 49. The summaries for these data are: n = 11, Y bar = 51.27,and s = 8.26,a. Calculate a 95% Confidence Interval for the mean age at first transplantb. Additionally, calculate the p-value for the Hypothesis Test Ho: = 50 vs. Ha 50 andtest this against =.10


Paper#61642 | Written in 18-Jul-2015

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