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. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.05 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.

Patient 1 2 3 4 5 6 7 8 9

Blood pressure (before) 160 189 185 193 166 199 193 178 156

Blood pressure (after) 142 174 159 181 160 173 171 170 141

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

Answer 1

1)

  

2) = (18 + 15 + 26 + 12 + 6 + 26 + 22 + 8 + 15)/9 = 16.4

s_d = sqrt(((18 - 16.4)^2 + (15 - 16.4)^2 + (26 - 16.4)^2 + (12 - 16.4)^2 + (6 - 16.4)^2 + (26 - 16.4)^2 + (22 - 16.4)^2 + (8 - 16.4)^2 + (15 - 16.4)^2)/8) = 7.2

3) Th test statistic is

4) df = 9 - 1 = 8

At alpha = 0.05, the critical value is t_0.05,8 = 1.860

Reject H₀, if t > 1.860

5) Since the test statistic value is greater than the critical value(6.833 > 1.860), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the new drug reduces the systolic blood pressure.