Ms. Fitness-Buff, a high school gym teacher, wants to propose an after-school fitness program. To get an idea of the fitness level of the students at her school, she takes a random sample of 75 students and records the number of hours the students exercised in the past week. Her sample mean is 2.25 hours and she knows from past research that the population standard deviation is 2 hours. She wants to know if this varies from a population mean of 3 hours/week.
A. Construct a 95% confidence interval.
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B. Draw a conclusion for a two-sided test at a = .05.
C. Ms. Fitness-Buff is told that if students exercise less than 3 hours per week, she can start an after-school fitness program. Test this one-sided hypothesis and draw a conclusion at a = .05.
D. What would the consequences of a Type I error be in the test from part C?
E. What’s the probability of a Type I error for the test in part C?
F. What would the consequences of a Type II error be for the test from part C?
G. What is the rejection region for Ho: mue = 3 for the test from part C?
H. Calculate the probability of making a Type II error if the true population mean is 2.75.
I. What’s the power of the test if the true population mean is 2.75?
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