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 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   Blood pressure (before)   Blood pressure (after)
1   175   154
2   182   157
3   175   161
4   202   191
5   187   175
6   169   149
7   170   152
8   177   169
9   185   169

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.

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% confidence interval. Round your answers to one decimal place.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Point estimate = 16.1

Step - 2: Standard deviation = 5.418589

Step - 3: Margin of error = (19.46982 - 12.752402)/2 = 3.358709

Step - 4: 90% confidence interval:

Lower limit = 12.8

Upper limit = 19.5