Question

Patient	1	2	3	4	5	6	7	8	9
Blood Pressure (before)	161	189	205	201	187	161	169	157	200
Blood Pressure (after)	152	169	193	195	163	141	149	142	178

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 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim?

Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.01α=0.01 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug.

1. State the null and alternative hypotheses for the test.

2. Find the value of the standard deviation of the paired differences

3. Compute the value of the test statistic

4. Determine the decision rule for rejecting the null hypothesis H0

5. Make the decision for the hypothesis test

Answer 1

1)
H0 : mud = 0
Ha: mud < 0

2)

std.dev = 6.2472

3)

t = dbar/(sd/sqrt(n))
= 16.4444/(6.2472/sqrt(9))
= 7.8968

4)

Reject H0 if t < −2.896

5)

Do not reject H0