Question

A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Using this data, find the 90%90% confidence interval for the true difference in blood pressure for each patient after taking the new drug. Assume that the blood pressures 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
Blood pressure (before)	172172	196196	197197	191191	181181	193193	205205	189189	157157
Blood pressure (after)	148148	170170	171171	169169	161161	181181	199199	177177	150150

Copy Data

Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1x1 be the blood pressure before taking the new drug andx2x2 be the blood pressure after taking the new drug and use the formula d=x2−x1d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4:

Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

step 3 of 4

Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4:

Construct the 90%90% confidence interval. Round your answers to one decimal place.

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	8.027729719
Sample Mean	-17.2222222
Sample Size	9
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	2.675909906
Degrees of Freedom	8
t Value	1.8595
Margin of Error	4.975983
Confidence Interval
Interval Lower Limit	-22.20
Interval Upper Limit	-12.25

Step 1 of 4:  the point estimate for the population mean of the paired differences is -17.2

Step 2 of 4: the sample standard deviation of the paired differences is 8.027730

step 3 of 4 the margin of error to be used in constructing the confidence interval is 4.975983

Step 4 of 4:the 90% confidence interval is (-22.2 ,-12.3)

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