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 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.

Patient	1	2	3	4	5	6	7	8	9
Blood pressure (before)	192	197	193	182	154	164	164	195	202
Blood pressure (after)	177	182	187	175	143	153	158	181	194

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 two decimal places.

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

The statistical software output for this problem is:

Hence,

Step - 1: Hypotheses:

H₀ : μ_D = 0
H_A : μ_D > 0

Step - 2: Standard deviation = 0.73

Step - 3: Test statistic = 2.190

Step - 4: Decision rule:

Reject Ho if t > 3.365

Step - 5: Fail to reject the null hypothesis