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=0.01 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) 98 100.1 99 98.9 100.7 98.8 98.7 Temperature (after) 97.8 99.5 99.3 98.1 100.2 98.4 98.2 Step 2 of 5 : Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.

Answer 1

Question:

Find the value of the standard deviation of the paired differences

Answer:

From the given data, the paired differences: d = Before - After are got as follows:

Subject	1	2	3	4	5	6	7
Before	98	100.1	99	98.9	100.7	98.8	98.7
After	97.8	99.5	99.3	98.1	100.2	98.4	98.2
paired differences: d = Before - After	0.2	0.6	- 0.3	0.8	0.5	0.4	0.5

From the values of d, the following Table is calculated:

d	(d - )	(d - )2
0.2	- 0.1857	0.0345
0.6	0.2143	0.0459
- 0.3	- 0.6857	0.4702
0.8	0.4143	0.1716
0.5	0.1143	0.0131
0.4	0.0143	0.0002
0.5	0.1143	0.0131
Total =		0.7486

The value of the standard deviation of the paired differences (s_d) is given by:

So,

Answer is:

0.35