Small Sample Difference of two means. Many companies installed exercise equipmen

Question

Small Sample Difference of two means.   Many companies installed exercise equipment to help with productivity. The idea is that healthier employees would be more productive. One company conducted a test to see if employees that exercised regularly had a higher level of productivity, as measured by their supervisors. Workers were randomly selected and then divided into two groups: those that exercised as least 3 times a week (EXER) and those that did not exercise (NONEXER). The study used a supervisor rating system for each employee, which ranged from 1 to 25, with 25 indicating a higher productivity rating. The Excel output for a difference of means test assuming equal variances is given below.

Exer

Nonexer

16.789

12.647

19.953

34.618

19

17

26.854

0

34

2.394

0.011

1.691

0.022

2.032

Assuming equal variances, the t-value for a 90 confidence interval of the difference of the two means is:

t-Test: Two-Sample Assuming Equal Variances

Exer

Nonexer

Mean

16.789

12.647

Variance

19.953

34.618

Observations

19

17

Pooled Variance

26.854

Hypothesized Mean Diff

0

df

34

t Stat

2.394

P(T<=t) one-tail

0.011

t Critical one-tail

1.691

P(T<=t) two-tail

0.022

t Critical two-tail

2.032

Explanation / Answer

C. 1.691. For df = 34 and confidence interval = 90%

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