In: Math
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, xi - yi
b) Do hypothesis testing to see if µd < 0 at the α = .025.
Part a)
Number | X values | Y values | Difference |
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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 :- µd = 0
H1 :- µd < 0
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 µd < 0.