Top swimming times for male members of a college team were found for various eve

Question

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 20.9 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 46.4 and a standard deviation of 0.8. Produce a 95% confidence interval (rounding to the nearest tenth).

(d) Based on your confidence intervals from parts (a) and (b), can top swimmers on average swim the 100 freestyle in twice the time it takes to swim the 50 freestyle?
Yes
No, apparently they average less than twice the time for the 100 compared to the 50.
No, apparently they average more than twice the time for the 100 compared to the 50

Explanation / Answer

a) 20.9 ± 2.78*0.4 = 20.9 ±1.1
b) 46.4 ±2.78*0.8 = 46.4 ±2.2
d) No, apparently they average more than twice the time for the 100 compared to the 50, since even if the actual time for the 50 was at the top end of the confidence interval (so it would be 20.9+1.1 = 22.0) and the actual time for the 100 was at the low end of the confidence interval (so it would be 46.4-2.2 = 44.2) the time for the 100 would still be more than twice the time for the 50 (44.2 > 2*22.0)

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