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)

199

166

183

197

200

192

190

179

200

Blood pressure (after)

183

151

172

174

185

170

180

173

185

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 H0. Round the numerical portion of your answer to three decimal places.

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

Answer 1

Before	After	Difference
199	183	16
166	151	15
183	172	11
197	174	23
200	185	15
192	170	22
190	180	10
179	173	6
200	185	15
	Total	133

Step 1:

A pharmaceutical company claims that its new drug reduces systolic blood pressure.

The null and alternative hypothesis is

Step 2:

Sample standard deviation of difference = = 5.4

Step 3:

Sample size = n = 9

Sample mean of difference = = 14.78

Test statistic is

Step 4:

Degrees of freedom = n - 1 = 9 - 1 = 8

Critical value = 1.860 ( Using t table)

Step 5:

Test statistic > critical value we reject null hypothesis.

Conclusion:

A pharmaceutical company claims that its new drug reduces systolic blood pressure is right.