Question

Use a t-distribution to find a confidence interval for the difference in means μd = μ1 - μ2 using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x1 - x2.

A 99% confidence interval for μd using the paired data in the following table:

Case	1	2	3	4	5
Treatment 1	22	29	30	24	28
Treatment 2	17	32	24	21	21

Give the best estimate for μd, the margin of error, and the confidence interval.

Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places.

best estimate = _______________

margin of error = _________________

The 99% confidence interval is _____________ to __________________

Answer 1

best estimate for

d: x₁ - x₂

n : Sample size = 5

Case	x1: Treatment 1	x2: Treatment 2	d=x1-x2
1	22	17	5
2	29	32	-3
3	30	24	6
4	24	21	3
5	28	21	7
		Total :	18
		:18/5 =3.6	3.6

best estimate for

Margin of Error :

for 99% confidence level = (100-99)/100 = 0.01

/2 = 0.01/2 = 0.005

Degrees of freedom = n-1= 5-1=4

For 4 degrees of freedom , t_0.005 = 4.6041

d=x1-x2	(d-d)	(d-d)2
5	1.4	1.96
-3	-6.6	43.56
6	2.4	5.76
3	-0.6	0.36
7	3.4	11.56
		Total: = 63.2

Margin of Error :

Margin of error = 8.18

The 99% confidence interval is:

best estimate = _3.6______________

margin of error = __8.18_______________

The 99% confidence interval is __________-4.58___ to ____11.78_______