Question

A medical researcher believes that a drug changes the body's temperature. Seven test subjects are randomly selected and the body temperature of each is measured. The subjects are then given the drug, and after 30 minutes, the body temperature of each is measured again. The results are listed in the table below. Is there enough evidence to conclude that the drug changes the body's temperature? Let d=(body temperature after taking drug)−(body temperature before taking drug). Use a significance level of α=0.05 for the test. Assume that the body temperatures are normally distributed for the population of people both before and after taking the drug. Subject 1 2 3 4 5 6 7 Temperature (before) 99.7 100.6 98.8 99.2 99.4 99.1 99 Temperature (after) 99.1 99.8 99.7 99 98.7 98.3 98.5 Step 4 of 5 : Find the p-value for the hypothesis test. Round your answer to four decimal places.

Answer 1

Hypothesis

H₀ : ( drug does not change the body's temperature )

H₁: ( drug changes the body's temperature )

level of significance alpha = 0.05

Let d=(body temperature after taking drug)−(body temperature before taking drug).

Subject	Temperature (before)	Temperature (after)	d
1	99.7	99.1	-0.6
2	100.6	99.8	-0.8
3	98.8	99.7	0.9
4	99.2	99	-0.2
5	99.4	98.7	-0.7
6	99.1	98.3	-0.8
7	99	98.5	-0.5

descriptive statistics

mean = - 0.386

standard deviation S_d = 0.604

test statistic t = = = -1.690

p-value = 0.1420

Since p-value is greater than significance level of α=0.05 we fail to reject null hypothesis and we conclude that there is insignificant evidence that drug changes the body's temperature.