Question

# Given two dependent random samples with the following results: Population 1 81 59 57 84 52...

Given two dependent random samples with the following results:

 Population 1 Population 2 81 59 57 84 52 62 65 80 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.

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:
μD = μ1 - μ2 : Mean of the difference between Pop 1 and Pop 2
H0 : μD = 0
HA : μD ≠ 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

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