Question

Given two dependent random samples with the following results:

Population 1	70	69	60	60	59	54	62	68
Population 2	79	59	66	52	66	59	55	70

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.02α=0.02 for the test. Assume that both populations are normally distributed.

Copy Data

Step 1 of 5 :  

State the null and alternative hypotheses for the test.

Step 2 of 5:

Find the value of the standard deviation of the paired differences.

Step 3 of 5:

Compute the value of the test statistic.

Step 4 of 5

Determine the decision rule for rejecting the null hypothesis Ho. Round to three decimals

Step 5 of 5

Make the decision for the hypothesis test

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-





t = -0.1857

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 0.1857 ) = 0.8579
Reject null hypothesis if P value < level of significance
P - value = 0.8579 > 0.02 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is not sufficient evidence to support the claim that there is a difference between the two population mean.