5 You take a random sample of 20 students at your school and find the average

5 you take a random sample of 20 students at your

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5. You take a random sample of 20 students at your school and find the average to be 530 with a standard deviation of 15. a. What parameter do you want to estimate, and at what confidence level? b. What inference method will you be using? Check the conditions. c. What is your 99% C.I.? d. Interpret the C.I. in the context of the problem. e. Is it plausible that the mean SAT Math score of all students is 550? Explain. 6. Ask young men to estimate their own degree of body muscle by choosing from a set of 100 photos. Then ask them to choose what they believe women prefer. The researchers know the actual degree of muscle, measured as kilograms per square meter of fat-free mass, for each of the photos. They can therefore measure the difference between what a subject thinks women prefer and the subject’s own self-image. Call this difference the “muscle gap.” Here are summary statistics for the muscle gap from a random sample of 200 American and European young men: mean = 2.35 and SD = 2.5 a. Calculate and interpret a 95% confidence interval for the mean size of the muscle gap for the population of American and European young men. (Follow parts a-d from number 5) b. A graph of the sample data is strongly skewed to the right. Explain why this information does not invalidate the interval you calculated in part (a). 7. High School students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points. How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work. 8. The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI in this population to within 1 unit with 99% confidence? Show your work.
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