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=0.1 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) 99.1 99.9 98 100.1 100.6 100.5 100.2

Temperature (after) 98.6 99.4 98.7 99.4 99.9 99.8 99.3

Step 2 of 5 : Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.

Answer 1

Null Hypothesis

Alternative Hypothesis

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

The Calculation table given below is

Subject	Temp.(Before)	Temp. (After)	d =After -Before	d^2
1	99.1	98.6	-0.5	0.25
2	99.9	99.4	-0.5	0.25
3	98	98.7	0.7	0.49
4	100.1	99.4	-0.7	0.49
5	100.6	99.9	-0.7	0.49
6	100.5	99.8	-0.7	0.49
7	100.2	99.3	-0.9	0.81
		Total	-3.3	3.27

The sample mean of paired differences

The sample standard deviation of paired differences

Undre H0, the test statistic is

Degrees of freedom = n-1= 6

Significance Level

The critical value of t for 6 df at 10% significance level is +/-1.943

The P-Value is .0584

Since p value is less than significance level, Reject H0.

Hence, at 10% level of significance we have enough evidence to conclude that the drug changes the body's temperature