Question

14. We are interested in the average escape time for firemen participating in a drill that involves escaping a dangerous situation. A random sample of 26 escape times is taken and gives a mean of 24.36 with a variance of 370.69. We wish to find a 95% confidence interval for the true mean escape time for firemen participating in this drill a) (5 pts.) Are any additional assumptions necessary? If so, what and why? If not, why not? You must be complete and specific to obtain full credit. b) (5 pts.) Assume anything you might have stated in (a) and calculate the appropriate interval Type hare

Answer 1

(a)

Yes. We must assume that the population from which the sample is drawn, is Normally distributed

(b)

Sample size(n)=26

Sample mean()=24.36

T

Sample SD(s)=$\sqrt{370.69}$=19.2533114

The 95% confidence interval is given by

lī * +0.025, n-1 n n

$i.e.\;\;(24.36\pm\frac{19.2533114}{\sqrt{26}}*t_{0.025,25})$

$i.e.\;\;(24.36\pm\frac{19.2533114}{\sqrt{26}}*2.059539)$

$i.e.\;\;(24.36\pm 7.776582459)$

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