Times (in seconds) for the 100 freestyle and 100 backstroke were recorded for three top swimmers on a university swim team: 46.18 and 50.02; 46.62 and 50.22; 46.89 and 52.85.
a. Assuming these to be representative samples of all top swimmers' times for the two events, use software to produce a 95% confidence interval for the mean of the time differences, freestyle minus backstroke, for the two events.
b. Report whether or not the interval contains zero, or only positive numbers, or only negative numbers.
c. What does your answer to part (b) suggest?