Confidence Interval for Difference between Two Population Means

After teaching at the U of I for a year, Alex notices that a lot of students take buses to go from one part of campus to another instead of walking. He believes that students who live on-campus tend to take the bus even more often, and hence, rarely walk!

To test this hypothesis, he randomly selects a sample of38students who live on-campus and a sample of36students who live off-campus. For each student in the sample, he asks them to wear a FitWatch (a smart watch that counts the number of steps taken) over a span of 2 weeks. The on-campus sample has a daily average of5168steps with a standard deviation of1042steps. The off-campus sample has a daily average6080steps with a standard deviation of1259steps.

Assume that the daily standard deviations of number of steps taken by students who live on-campus and off-campus are the same.

Construct a 90% (two-sided) confidence interval for the true difference in the daily average steps of students who live on-campus and off-campus (on-campus - off-campus).