Question

twenty torpedoes are released in an underwater war exercise. Fifteen of them hit their target. Find a 90% confidence interval for the probability of a torpedo hitting the target.

a. Use the Exact Confidence Interval for a Binomial table to solve this problem.

b. Use the large sample approximation to solve this problem

c. Discuss the assumptions you are making in this problem

Answer 1

Here we have

n=20, y = 15

(a)

Using table (row n=20, Y=15 and column 90% confidence interval), the exact confidence interval is,

(0.544, 0.896)

That is lower bound: 0.544

Upper bound: 0.896

(b)

Sample proportion is

For 90% confidence interval, using excel function "=NORMSINV(0.95)", critical value of z will be
---------------------------

Confidence interval for population proportion will be

(c)

The assumption is sampling distribution of sample peroprotion is normally distributed.