Question

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

Using the date find the 90% confidence interval for the true difference in blood pressure for each patient taking the new drug. Assume that the blood pressures are normally distributed for the population of patients both before and after taking the new drug.

Blood pressure before 199, 181, 153, 168, 202, 194, 175, 191, 189

Blood pressure after 173, 162, 144, 156, 193, 170, 166, 176, 171

Construct the 90% confidence interval.

Answer 1

Before	After	Difference
199	173	26
181	162	19
153	144	9
168	156	12
202	193	9
194	170	24
175	166	9
191	176	15
189	171	18

∑d = 141

∑d² = 2549

n = 9

Mean , x̅d = Ʃd/n = 141/9 = 15.6667

Standard deviation, sd = √[(Ʃd² - (Ʃd)²/n)/(n-1)] = √[(2549-(141)²/9)/(9-1)] = 6.5192

90% Confidence interval :

At α = 0.1 and df = n-1 = 8, two tailed critical value, t-crit = T.INV.2T(0.1, 8) = 1.860

Lower Bound = x̅d - t-crit*sd/√n = 15.6667 - 1.86 * 6.5192/√9 = 11.626

Upper Bound = x̅d + t-crit*sd/√n = 15.6667 + 1.86 * 6.5192/√9 = 19.708

11.626 < µd < 19.708