Question

When subjects were treated with a​ drug, their systolic blood pressure readings​ (in mm​ Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Using a0.01 significance​ level, is there sufficient evidence to support the claim that the drug is effective in lowering systolic blood​ pressure?

Before	210	188	175	157	175	164	155	189	188	205	159	167
After	179	179	162	152	188	148	176	155	147	143	163	177

In this​ example, μd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the systolic blood pressure reading before the drug was taken minus the reading after the drug was taken. What are the null and alternative hypotheses for the hypothesis​ test? What is the T statistic? What is the P-value? What is the conclusion?

Answer 1

H0:Null Hypothesis: ( the drug is not effective in lowering systolic blood​ pressure )

HA; Alternative Hypothesis: ( the drug is effective in lowering systolic blood​ pressure ) (Claim)

From the given data, values of d = Before - After are got as follows:

d = Before - After = 31, 9, 13, 5, - 13, 16, - 21, 34, 41, 62, - 4,-10

From d values, the following statistics are calculated:

n =12

= 13.583

s_d = 24.652

test statistic is given by:

df = 12 - 1 = 11

One Tail - Right Side Test

By Technology, P - value = 0.0414

Since P - value = 0.0414 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

The data do not support the claim that the drug is effective in lowering systolic blood​ pressure.