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In: Statistics and Probability

A sample of Alzheimer's patients is tested to assess the amount of time in stage IV...

A sample of Alzheimer's patients is tested to assess the amount of time in stage IV sleep these patients get in a 24-hour period. Number of minutes spent in Stage IV sleep is recorded for 61 patients. The mean stage IV sleep over a 24 hour period of time for these 61 patients was 48 minutes with a standard deviation of 14 minutes.

(a) Compute 95% confidence interval for mean stage IV sleep. Interpret this confidence interval.

(b) It has been believed that individuals suffering from Alzheimer's Disease may spend less time per night in the deeper stages of sleep. Test the hypothesis at 5% significance level if the true mean stage IV sleep of Alzheimer patients is less than 50 minutes.

Provide the hypothesis statement

Calculate the test statistic value

Determine the probability value

(c) Could the confidence interval in part (a) be used to test the hypothesis in part (b)? Why or why not? (1 mark)

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