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=0.01 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)	179	192	187	175	193	181	158	164	192
Blood pressure (after)	171	179	177	163	183	164	149	148	186

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

here, we will do paired t test

hypothesis:-

where , is the difference between blood pressure before taking new drug and blood pressure after taking new drug.

the necessary calculation table be:-

before()	after()
179	171	8	10.38257
192	179	13	3.16057
187	177	10	1.49377
175	163	12	0.60497
193	183	10	1.49377
181	164	17	33.38297
158	149	9	4.93817
164	148	16	22.82737
192	186	6	27.27137
		sum=101	sum=105.55556

number of observations(n) = 9

the value of the standard deviation of the paired differences be:-

the test statistic be:-

[ for more accurate calculation i have used the sd = 3.6324 in spite of 6.3]

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

t critical value for df = 8,alpha=0.01, right tailed test be:-

[from t distribution table]

decision rule:-

reject the null hypothesis if,

decision:-

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to support the claim that its new drug reduces systolic blood pressure at 0.01 level of significance.

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