Question

Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d=x-​y, find d overbar​, s Subscript d​, the t test​ statistic, and the critical values to test the claim that mu Subscript d=0.

x 6 17 3 13 15 13 8 18

y 6 14 8 12 12 8 6 15

d=_______

​(Round to three decimal places as​ needed.)

ds=______

​(Round to three decimal places as​ needed.)

t=________

​(Round to three decimal places as​ needed.)

tα/2=± ________

​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Before	after	difference
6	6	0
17	14	3
3	8	-5
13	12	1
15	12	3
13	8	5
8	6	2
18	15	3

So , data for differences is

0,3,-5,1,3,5,2,3

1)

= mean of (0,3,-5,1,3,5,2,3) = 1.500

= 1.500

2)

d_s = standard deviation of (0,3,-5,1,3,5,2,3) = 3.024

d_s = 3.024

3)

Test statistic

t = [1.500 - 0]/[3.024/8] = 1.403

t = 1.403

4)

df = n - 1 = 8 - 1 = 7

= 0.054

/2 = 0.25

Using t table ,

tα/2= ± 2.365