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) 187 186 176 203 182 168 199 167 204 Blood pressure (after) 178 166 158 187 157 159 192 148 196 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

Calculate the difference in the Blood Pressures d = X2 - X1

Step 1:   Mean of the difference d is calculated using Excel function average                  
   Mean of d = average(all ds) = -14.5556                  
   Point estimate for the population mean of the paired differences =                
                      
Step 2:   99% confidence interval                  
   We first find the sample standard deviation using excel funtion stdev.s                  
   s = stdev.s(all ds) = 6.4636                  

Given
X̅ = -14.5556           ....... Sample Mean
n = 9           ....... Sample Size
s = 6.4636           ....... Sample Standard Deviation

Since the population standard deviation is unknown, we use the t-distribution

Degrees of Freedom = df = n - 1 = 9 - 1 = 8

For 99% Confidence interval
α = 0.01,      α/2 = 0.005
From t tables of Excel function T.INV.2T (α, degrees of freedom) we find the t value
t = T.INV.2T (0.01, 8) = 3.355
We take the positive value of t

Confidence interval is given by

= (-21.7841, -7.3271)

99% Confidence interval is

Conclusion:

It can be seen from the confidence interval that both the lower and upper limits are negative.

This means that 99% of the times the confidence interval will have the true mean difference less than 0

that is the Blood Pressure after taking the drug will be less than the blood pressure before taking the drug.

implies that the drug reduces the blood pressure