Question

A random sample of drug addicts in Seattle participated in a program to reduce drug dependency. Time 1 is a measure of the number of illegal drugs they took per day before participating in the program. Time 2 is a measure of the number of illegal drugs they took after participating in the program. You have been hired to evaluate the success of the program. You hypothesize that the average number of illegal drugs consumed by the addicts after participating in the program will decrease compared to the average number of illegal drugs consumed prior to participating in the program. Below are the data.

Calculate the degrees of freedom. Df =

Time 1 (drugs taken before program)	Time 2 (drugs taken after participating in the program)	Difference	D2
2.00	1.00	-1	1
3.00	4.00	1	1
3.00	3.00	0	0
4.00	5.00	1	1
4.00	3.00	-1	1
5.00	3.00	-2	4
Sum = 21	Sum = 19	Sum = -2	Sum = 8
Mean = 3.5	Mean = 3.17	Mean = -.33	Mean = 1.33

	a.	12
	b.	15
	c.	5

Answer 1

Given that,

Time 1 (drugs taken before program)	Time 2 (drugs taken after participating in the program)	Difference	D2
2.00	1.00	-1	1
3.00	4.00	1	1
3.00	3.00	0	0
4.00	5.00	1	1
4.00	3.00	-1	1
5.00	3.00	-2	4
Sum = 21	Sum = 19	Sum = -2	Sum = 8
Mean = 3.5	Mean = 3.17	Mean = -.33	Mean = 1.33

Here, n = 6

Since it is paired t-test,

Degrees of freedom (DF) = n - 1 = 6 - 1 = 5

Therefore,

Answer: c) 5