Refer to Exercise 10.32. Construct a lower 95% one-sided confidence bound for the difference in the average times for the two swimmers. Does this interval confirm your conclusions in Exercise 10.32?
Exercise 10.32
In an effort to compare the average swimming times for two swimmers, each swimmer was asked to swim freestyle for a distance of 100 yards at randomly selected times. The swimmers were thoroughly rested between laps and did not race against each other, so that each sample of times was an independent random sample. The times for each of 10 trials are shown for the two swimmers.

Suppose that swimmer 2 was last year's winner when the two swimmers raced. Does it appear that the average time for swimmer 2 is still faster than the average time for swimmer 1 in the 100-yard freestyle? Find the approximate p-value for the test and interpret the results.

Swimmer 1 Swimmer 2 59.62 59.74 59.81 59.41 59.48 59.43 59.65 59.72 59.76 59.50 59.50 5963 6001 59.68 59.32 59.63 59.64 59.83 59.86 59.51