Question

Given two dependent random samples with the following results:

Population 1	69	55	53	56	59	74	76	71
Population 2	75	53	58	53	64	77	72	77

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=0.02  for the test. Assume that both populations are normally distributed.

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. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test. Reject or Fail to reject Null Hypothesis.

Answer 1

step 1:

null Hypothesis:μd		=	0
alternate Hypothesis: μd		≠	0

Step 2 of 5:

Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =

4.3

Step 3 of 5: Compute the value of the test statistic =-1.316 (please try -1.323 if this comes wrong and reply)

Step 4 of 5 :

Decision rule: reject Ho if absolute value of test statistic |t|>2.998

Step 5 of 5: fail to reject ho