Question

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 90% 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 10% significance level if the true mean stage IV sleep of Alzheimer patients is less than 49 minutes.

1. Provide the hypothesis statement
2. Calculate the test statistic value
3. Determine the probability value

Answer 1

(a) The 90% confidence interval for mean stage IV sleep is between 45.01 and 50.99.

We are 90% confident that the true mean stage IV sleep is between 45.01 and 50.99.

(b) The hypothesis being tested is:

H0: µ = 49

Ha: µ < 49

The p-value is 0.2895.

Since the p-value (0.2895) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the true mean stage IV sleep is less than 49 minutes.

Yes, the confidence interval can be used. Since the confidence interval is above 50 minutes, we cannot conclude that the true mean stage IV sleep is less than 49 minutes.

49.00	hypothesized value
48.00	mean 1
14.00	std. dev.
1.79	std. error
61	n
60	df
-0.558	t
.2895	p-value (one-tailed, lower)
45.01	confidence interval 90.% lower
50.99	confidence interval 90.% upper
2.99	margin of error