Question

The efficacy of salt-free diets for controlling high blood pressure is studied for a sample of 8 patients.

Each has their diastolic blood pressure measured before going on the diet and after. The data appear below:

Patient	1	2	3	4	5	6	7	8
Sample 1 - Before	93	106	90	93	102	95	88	110
Sample 2 - After	92	102	89	92	101	96	87	105

Assume the differences in blood pressure fit a normal distribution.

Use the matched pairs test and a 0.05 significance level to test the claim that the blood pressure before the diet is higher than the blood pressure after going on the diet.

a) Identify the Null and Alternative Hypotheses.

b) Find the critical value for the test.

c) Calculate the test statistic. Round off the descriptive statistics to one decimal place. Round off your test statistic to three decimal places.

d) What is your decision about the null hypothesis?

e) Write your conclusion about the claim.

What more data is required?

Answer 1

a)

Let we find blood pressure difference between them, Xd= blood pressure before - blood pressure after.

Xd follows a distribution with mean d.

H0: d= 0 , blood pressure before the diet is same with the blood pressure after going on the diet

Ha: d > 0 blood pressure before the diet is higher than the blood pressure after going on the diet

The test is one tail paired t test.

b)

t crit  = t=0.05,7 = 1.895

c)

differences are , Xdi = 1, 4, 1, 1, 1, -1, 1, 5

Mean of the differences= = Xd / n = 13 / 8 = 1.6

Variance of the differences=Sd ^2= ( Xd^2 ) - n* ^2 / (n-1) = 3.7

Sd = 1.9

Standard error of = SE( ) = Sd / = 1.9 / = 0.7

t = /SE( ) = 1.6 /0.7= 2.391

| t crit  | < | t |

d)

So, we reject null hypothesis.

e)

blood pressure before the diet is higher than the blood pressure after going on the diet.

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