Two Population Means

Question

At a recent faculty meeting, we were wondering if freshmen have more free time than seniors. We took a sample of 25 freshmen and 23 seniors. Each student was asked to record the amount of free time he or she had in a typical week. The mean for the freshmen was found to be 29 hours of free time per week with a standard deviation of 7.0 hours. For the seniors, the mean was 22 hours of free time per week with a standard deviation of 6.2 hours. Assume that the two populations are normally distributed with equal but unknown population standard deviations. Test at a 5% significance level whether the two-population means are different.

If This Problem Calls for:	Use Test Statistic	Use Degrees of Freedom
Pooled Variance Test	3.897	Calculate your own
Separate Variance Test	3.655	46
Paired Samples Test	2.546	Calculate your own
Chi-squared Test	Calculate your own	Calculate your own

Answer 1

This is a two sample t test

Ho: MuF - MuS = 0

Ha: MuF - MuS not equal to 0

MuF - MuS = Actual difference in the means of hours per week of free time for Freshman minus seniors

Assuming two random samples, normality and independence, reject Ho if the calculated t > critical t

t calculated = (29-22)/sqrt((7^2/25)+(6.2^2/23)) = 3.67

t critical = t (df=46 alpha=0.025 two tailed)= 2.013

t calculated > t critical, Reject Ho. There is evidence that the two means are different