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In: Statistics and Probability

The following review problem is on hypothesis testing. Freshmen tend to gain 15 pounds during their first year in college

 

The following review problem is on hypothesis testing. Freshmen tend to gain 15 pounds during their first year in college. However, they try to improve their health during their sophomore year. Let X denote the weight loss of sophomores after taking an intensive year-long PE class. Assume that X is normally distributed with unknown mean µ and standard deviation 4. Weight loss of 14 students are recorded. To see if the students do lose their weight, we can test the null hypothesis H0 : µ = 0 against the alternative hypothesis that HA : µ > 0.

(a) What is the power of the hypothesis test if the true population mean were µ = 5, where α = 0.05?

(b) Find the sample size n that is necessary to achieve 0.90 power at the alternative µ = 5.

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orchestra answered 2 years ago
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