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 3030 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)d=(body temperature after taking drug)−(body temperature before taking drug). Use a significance level of α=0.02 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)	100.4	99.3	97.6	100.7	99.6	99.7	98.9
Temperature (after)	100.1	98.8	98	100.3	99.2	99.2	98.7

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Step 4 of 5 :  

Find the p-value for the hypothesis test. Round your answer to four decimal places.

Answer 1

Subject	Temperature(Before)	Temperature(After)	d	d2
1	100.4	100.1	-0.3	0.09
2	99.3	98.8	-0.5	0.25
3	97.6	98	0.4	0.16
4	100.7	100.3	-0.4	0.16
5	99.6	99.2	-0.4	0.16
6	99.7	99.2	-0.5	0.25
7	98.9	98.7	-0.2	0.04
		Total	-1.9	1.11

We have to test

H₀: µ_after - µ_before =0 i.e.

H_A: µ_after - µ_before ≠ 0 i.e.

We have got

n=7

Σd=-1.9

Σd²=1.11

The test statistic to test this null hypothesis is paired t-test given as below:

The value of test statistic, t = -2.2818

The p-value for above test is 0.0626

The above p-value is greater than α=0.02 which indicates that we do not have enough evidence against null hypothesis to reject it, so we fail to reject the null hypothesis and we can conclude that the drug does not changes the body's temperature.