Question

A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects nine patients and records the number of hours of sleep each gets with and without the new drug. The results of the two-night study are listed below. Using this data, find the 90% confidence interval for the true difference in hours of sleep between the patients using and not using the new drug. Let d=(hours of sleep with the new drug)−(hours of sleep without the new drug). Assume that the hours of sleep are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Hours of sleep without the drug 5.3 2.7 6.3 4.4 3.1 5.6 6.1 4.5 5.9 Hours of sleep with the new drug 7.6 3.7 8 6.3 5.1 7.5 7.1 6.8 7.5 Step 2 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places

Answer 1

using excel>addin>phstat>confidece interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.482470494
Sample Mean	1.744444444
Sample Size	9
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	0.160823498
Degrees of Freedom	8
t Value	1.8595
Interval Half Width	0.2991
Confidence Interval
Interval Lower Limit	1.45
Interval Upper Limit	2.04

the critical value that should be used in constructing the confidence interval is 1.860

90% confidence interval is (1.45 ,2.04)