Question

Given two dependent random samples with the following results:

Population 1   Population 2
53   57
60   55
79   82
78   68
56   65
68   73
60   51
66   76

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)

. Use a significance level of α=0.02

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

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.

Answer 1

Hypothesis Test: Paired Observations
	0.000	hypothesized value
	65.000	mean Population 1
	65.875	mean Population 2
	-0.875	mean difference (Population 1 - Population 2)
	7.846	std. dev.
	2.774	std. error
	8	n
	-0.32	z
	.7524	p-value (two-tailed)
	-7.328	confidence interval 98.% lower
	5.578	confidence interval 98.% upper
	6.453	margin of error

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: 7.8

Compute the value of the test statistic. Round your answer to three decimal places.

Test statistic: -0.315

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis H0

Since p value>alpha

We fail to reject the null hypothesis

. Round the numerical portion of your answer to three decimal places.

Step 5 of 5:

Make the decision for the hypothesis test.

There is not sufficient evidence to conclude that  there is a difference between the two population means