As we saw in chapter 8, Exercise 40, between 1954 and 2013, swimmers have crossed Lake Ontario 58 times. Both women and men have made the crossing. Here are some plots (we've omitted a crossing by Vikki Keith, who swam a round trip€”North to South to North€”in 3390 minutes):

Summary statistics are as follows

Is there a difference between the mean amount of time (in minutes) it takes female and male swimmers to swim the lake?
a) Construct and interpret a 95% confidence interval for the difference between female and male crossing times (technology gives 35.7 df).
b) Comment on the assumptions and conditions and your conclusions.

Women 2500 2000 1500 1000 10 1000 1500 2000 1000 1500 2000 2500 Time (min) Time (min) Summary of Time (min) Group Count Mean StdDev 34 1257.09 261.10 23 1226.04 382.85