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) 199 164 173 201 174 163 172 155 182

Blood pressure (after) 186 153 147 189 167 151 154 142 162

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. Reject or Fail to Reject

Answer 1

Step 1 of 5: The null and alternative hypotheses for the test are as below

H₀ : There is no sufficient evidence that new drug reduces systolic blood pressure.

H₁ : There is sufficient evidence that new drug reduces systolic blood pressure.

Consider,  

is diffrence between the both population means that is ()

Using parameter the null and alternative hypotheses for the test

Step 2 of 5: We find the value of the standard deviation of the paired differences using following table

Let, = Blood pressure (before)

= Blood pressure (after)

199	186	13	169
164	153	11	121
173	147	26	676
201	189	12	144
174	167	7	49
163	151	12	144
172	154	18	324
155	142	13	169
182	162	20	400
		132	2196

We find mean () and standard deviation () using following formula

(Round answer up to 1 decimal places)

Step 3 of 5: We compute the value of the test statistic using following formula

If we used then test statistic are as below

(Round answer up to 3 decimal places)

Or

If we used then test statistic are as below

(Round answer up to 3 decimal places)

Test statistic

If we used

If we used

(Because in the above question it is not given the answer of mean () round up to which decimal places)

Step 4 of 5: We determine the decision rule for rejecting the null hypothesis H0 are as below

First we find critical value of t using t table whose level of significance = α = 0.05 (For one tailed test) and

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

Critical value of t = 1.860

We comparing above critical value of t with the test statistic and take decision about the reject or do not reject the null hypothesis H₀ are as below

If test statistic t critical value of t then we reject the null hypothesis H₀ otherwise we fail to reject the null hypothesis H₀.

Here, Test statistic    or      Critical value of t = 1.860

Step 5 of 5: We make the decision for the hypothesis test are as below

Here, Test statistic    or      Critical value of t = 1.860

We reject the null hypothesis H₀.

That is, There is sufficient evidence that new drug reduces systolic blood pressure.

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