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 2 hours after taking the drug are shown in the table below. Using this data, find the 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)	192	197	193	182	154	164	164	195	202
Blood pressure (after)	177	182	187	175	143	153	158	181	194

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Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1 be the blood pressure before taking the new drug and xx2 be the blood pressure after taking the new drug and use the formula d=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 99% confidence interval. Round your answers to one decimal place.

Answer 1

step 1:

dbar =-10.3

step 2:

sd =3.741657

step 3:

for 99% CI; and 8 degree of freedom, value of t=			3.355
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		4.184420

step 4:

lower confidence limit                     =		-14.5
upper confidence limit                    =		-6.1