Question

In: Math

Consider the following dependent random samples Observations           1        2        3       4 &

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.

Solutions

Expert Solution

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 :- µd = 0

H1 :- µd < 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 µd < 0.


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