Question

Given two dependent random samples with the following results:

Population 1	81	59	57	84	52	62	65	80
Population 2	85	53	66	82	54	64	57	84

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

The statistical software output for this problem is:

Summary statistics:

Column	n	Mean	Variance	Std. dev.
Differences	8	-0.625	31.696429	5.6299581

Paired T hypothesis test:
μ_D = μ₁ - μ₂ : Mean of the difference between Pop 1 and Pop 2
H₀ : μ_D = 0
H_A : μ_D ≠ 0
Hypothesis test results:

Difference	Mean	Std. Err.	DF	T-Stat	P-value
Pop 1 - Pop 2	-0.625	1.9904908	7	-0.31399291	0.7627

Hence,

2) Standard deviation = 5.6

3) Test statistic = -0.314

4) Decision rule: Reject Ho if |t| > 2.998

5) Fail to Reject Null Hypothesis