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 99%99% 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)	199199	166166	183183	197197	200200	192192	190190	179179	200200
Blood pressure (after)	183183	151151	172172	174174	185185	170170	180180	173173	185185

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 and x2x2 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: Find the SD

Step 3: Find the Margin Error

Step 4: find the interval confidence

Answer 1

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*S_D/sqrt(n)

Step 1 of 4 :  

From given data, we have

Dbar = -14.7777778

(by using excel)

The point estimate for the population mean of the paired differences = -14.7777778

Step 2: Find the SD

S_d = 5.426273532

(by using excel)

n = 9

df = n – 1 = 8

Confidence level = 99%

Critical t value = 3.3554

(by using t-table)

Step 3: Find the Margin Error

Margin of error = t*S_D/sqrt(n)

Margin of error = 3.3554*5.426273532/sqrt(9)

Margin of error = 3.3554* 1.808757844

Margin of error = 6.0691

Step 4: find the interval confidence

Confidence interval = Dbar ± t*S_D/sqrt(n)

Confidence interval = -14.7777778 ± 3.3554*5.426273532/sqrt(9)

Confidence interval = -14.7777778 ± 6.0691

Lower limit = -14.7777778 - 6.0691 = -20.85

Upper limit = -14.7777778 + 6.0691 = -8.71

-20.85 < µ_d < -8.71