Homework SourseSmall Sample Difference of two means Many companies installe
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 |
Solution
C. 1.691. For df = 34 and confidence interval = 90%
