Help me please! Urgent! TV network executives are planning their coverage of the next Summer Olympics.

Question

TV network executives are planning their coverage of the next Summer Olympics. They randomly selected 675 people and asked them to name their favorite discipline in the Summer Olympics. In this sample, 255 people said their favorite discipline was track and field. Find a 99% confidence interval for p, the proportion of people whose favorite discipline in the Summer Olympics in track and field.

A) 0.330<p<0.426

B) 0.331<p<0.427

C) 0.332<p<0.428

Answer 1

Using a beta distribution the answer is

This is the correct, unbiased, exact solution.

Normal approximation is close... The answer is b

note: for normal aproximation you need n (675), p(1/3), q(2/3) and the proper critical Z value for two sided 99% Confidence) Zcrit = 2.576. Then follow the standard formula for CI of a proportion.