Given two dependent random samples with the following results:
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:
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:
|Pop 1 - Pop 2||-0.625||1.9904908||7||-0.31399291||0.7627|
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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