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. 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 Assuming equal variances, the t-value for a 90 confidence interval of the difference of the two means is: A.1.960 B.2.032 C.1.691 D.1.645

Explanation / Answer

90% confidence interval for the difference between two population means assuming the twp populations have equal variances is:

(Xbar - Ybar) ± [tn1 + n2 - 2, 0.05 x s x sqrt{(1/n1) + (1/n2)}], whereXbar and Ybar are the two sample means, s is the pooled sample standard deviation, n1 and n2 are the two sample sizes and tn1 + n2 - 2, 0.05 = upper 5% point of t distribution with degress of freedom = n1 + n2 - 2.

Given, n1 = 19 and n2 = 17, n1 + n2 - 2 = 34.

So, t-value for 90% confidence interval for the difference between two population means is upper 5% point of t34

Usong Excel Function, this value is found to be 2.032 ANSWER option B.

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