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=0.1 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) 201 190 177 193 201 167 170 168 183 Blood pressure (after) 184 166 171 185 180 152 149 157 159

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

The statistical software output for this problem is:

Paired T hypothesis test: HD 1-2 Mean of the difference between Before and After Ho Hp 0 HA HD 0 Hypothesis test results: Difference Std. Err. DF T-Stat P-value Mean Before - After 16.333333 2.2607767 8 7.2246559 0.0001|

Hence,

Step - 2: Standard deviation = 6.8

Step - 3: Test statistic = 7.225

Step - 4: Reject Ho if t > 1.397

Step - 5: Reject Null Hypothesis