Question

A pharmaceutical company is testing a new cold medicine to determine if the drug has side affects. To test the drug, 8 patients are given the drug and 9 patients are given a placebo (sugar pill). The change in blood pressure after taking the pill was as follows:

Given drug: 3 4 5 1 -2 3 5 6

Given placebo: 1 -1 2 7 2 3 0 3 4

Test to determine if the drug raises patients’ blood pressure more than the placebo using α = 0.01

Answer 1

H0: Mean blood pressure raised by drug is equal to mean blood pressure raised by placebo.

H1: Mean blood pressure raised by drug is greater than the mean blood pressure raised by placebo.

Since we do not know the population standard deviation, we will use independent samples t test.

Sample means are,

= (3 + 4 + 5 + 1 - 2 + 3 + 5 + 6) / 8 = 3.125

= (1 -1 + 2 + 7 + 2 + 3 + 0 + 3+ 4) /9 = 2.333

Sample standard deviations are,

s1 = sqrt{[((3 - 3.125)² +  (4 - 3.125)² +  (5 - 3.125)² +  (1 - 3.125)² +  ( - 2 - 3.125)² +  (3 - 3.125)² +  (5 - 3.125)² +  (6 - 3.125)² ] / 7} = 2.587746

s2 = sqrt{[(1 - 2.333)² + (-1 - 2.333)² + (2 - 2.333)² + (7 - 2.333)² + (2 - 2.333)² + (3 - 2.333)² + (0 - 2.333)² + (3 - 2.333)² + (4 - 2.333)² ] /8} = 2.345208

Standard error of mean difference , SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]

SE = sqrt[(2.587746²/8) + (2.345208²/9)] = 1.203397

Degree of freedom is,

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

DF = (2.587746²/8 + 2.345208²/9)² / { [ (2.587746² / 8)² / (8 - 1) ] + [ (2.345208² / 9)² / (9 - 1) ] }

= 14 (Rounding to nearest integer)

Test statistic, t = (3.125 - 2.333) / 1.203397 = 0.6581

P-value = P(t > 0.6581, df = 14) = 0.2606

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that mean blood pressure raised by drug is greater than the mean blood pressure raised by placebo.