Question

Consider the following dependent random samples
Observations           1        2        3       4        5        6
x-values                  8.8    7.9     8.0     8.4    8.2    8.0
y-values    7.7    7.3 8.0     8.9    7.5      7.8

a) Determine the difference between each set of points, x_i - y_i

b) Do hypothesis testing to see if µ_d < 0 at the α = .025.

Answer 1

Part a)

Number	X values	Y values	Difference
	8.8	7.7	1.1	0.5625
	7.9	7.3	0.6	0.0625
	8	8	0	0.1225
	8.4	8.9	-0.5	0.7225
	8.2	7.5	0.7	0.1225
	8	7.8	0.2	0.0225
Total	49.3	47.2	2.1	1.615

Part b)

To Test :-

H0 :- µ_d = 0

H1 :- µ_d < 0

Test Statistic :-





t = 1.5085

Test Criteria :-
Reject null hypothesis if
Critical value
= 1.5085 > -2.57058183563632
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.5085 ) = 0.9041
Reject null hypothesis if P value < level of significance
P - value = 0.9041 > 0.025 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that µ_d < 0.