Question

Assume that the differences are normally distributed. Complete parts ​(a) through ​(d) below.

Observation   Xi Yi
1 48.8 51.1
2 47.4 48.7
3 48.2 50.1
4 48.0 52.1
5 48.6 48.5
6 49.8 53.6
7 51.7 52.8
8 54.3 53.5

(a) Determine di = Xi−Yi for each pair of data. (Type integers or​ decimals.)

di 1__ 2__ 3__ 4__ 5__ 6__ 7__ 8__

(b)Compute d overbard and sd.

d overbard = __ ?

sd = __?

(c)

Test if μd <0 at the α =0.05 level of significance.

(d) find the P value (rounded to three decimal places)

Answer 1

Number	Before	After	Difference
	48.8	51.1	-2.3	0.36
	47.4	48.7	-1.3	0.16
	48.2	50.1	-1.9	0.04
	48	52.1	-4.1	5.76
	48.6	48.5	0.1	3.24
	49.8	53.6	-3.8	4.41
	51.7	52.8	-1.1	0.36
	54.3	53.5	0.8	6.25
Total	396.8	410.4	-13.6	20.58

Test Statistic :-

To Test :-

H0 :-  

H1 :-


t = -2.8043

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 1.7518 ) = 0.013
Reject null hypothesis if P value < level of significance
P - value = 0.013 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis