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) 194 164 201 185 199 179 198 177 190 Blood pressure (after) 171 145 192 172 187 158 174 168 168 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 x2 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.

Answer 1

Let x1 be the blood pressure before taking the new drug and x2 be the blood pressure after taking the new drug and use the formula d=x2−x1 to calculate the paired differences

using minitab>stat>basic stat>paired t

we have

Paired T-Test and CI: bp(before), bp(after)

Paired T for bp(before) - bp(after)

N Mean StDev SE Mean
bp(before) 9 187.44 12.32 4.11
bp(after) 9 170.56 14.00 4.67
Difference 9 16.89 6.11 2.04

99% CI for mean difference: (10.05, 23.73)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 8.29 P-Value = 0.000

the point estimate for the population mean of the paired differences is 16.89

the 99% confidence interval for the true difference in blood pressure for each patient after taking the new drug is (10.05, 23.73)