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.

Answer 1

Before	after	d= before-after	(d-dbar)^2
93 106 90 93 102 95 88 110	92 102 89 92 101 96 87 105	1 4 1 1 1 -1 1 5 M: 1.62	0.39 5.64 0.39 0.39 0.39 6.89 0.39 11.39 S: 25.88

a) null and alternate hyothesis

H0:d0

H1:d>0

b) tthe critical value = 2.364

C) test statistics

Mean: 1.62
μ = 0
S² = SS⁄df = 25.88/(8-1) = 3.7
S²_M = S²/N = 3.7/8 = 0.46
S_M = √S²_M = √0.46 = 0.68

T-value Calculation

t = (M - μ)/S_M = (1.62 - 0)/0.68 = 2.39

D) since t = 2.39> 2.36 so we reject the null hypothesis .

E)so there sufficient evidenceeto conclude that the blood pressure before the diet is higher than the blood pressure after going on the diet.