Question

In Star Trek, the original series, Captain Kirk was often depicted ignoring the prime directive of non-interference in other cultures. To determine if the crew approved of this 25 crew members were asked and 10 approved of the captain's methods. Find a 99% confidence interval for the true proportion of crew members who approve of Captain Kirk.

Answer 1

Solution :

Given that,

n = 25

x = 10

Point estimate = sample proportion = = x / n = 10 / 25 = 0.4

= 1 - = 1 - 0.4 = 0.6

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 (((0.4 * 0.6) / 25)

= 0.252

A 99% confidence interval for population proportion p is ,

± E

0.4 ± 0.252

(0.148 , 0.652)