Top swimming times for male members of a college team were found for various events. For these problems, use the fact that the t multiplier for 95% confidence and 4 degrees of freedom is 2.78.
a. Times for the top five swimmers of the 50 freestyle had a mean of 20.7 and a standard deviation of 0.4. Produce a 95% confidence interval (rounding to the nearest tenth).
b. Times for the top five swimmers of the 100 freestyle had a mean of 46.0 and a standard deviation of 0.9. Produce a 95% confidence interval (rounding to the nearest tenth).
c. Should we consider the population to be times for all male college swim team members in the given event?
d. Use your confidence intervals from parts (a) and (b) to argue whether or not top swimmers on average can swim the 100 freestyle in twice the time it takes to swim the 50 freestyle.