Question

A random sample of 200 apples was taken from an orchard and 30 were found rotten. Form a 99% confidence interval for the proportion of rotten apples in the orchard

Answer 1

n = sample size = number of apples = 200

x = number of rotten apples = 30

c = confidence level = 99% = 0.99

Proportion of rotten apples

The formula of a confidence interval for the proportion

Z - critical value at given confidence level.

alpha = 1 - c = 1 - 0.99 = 0.01

alpha/2 = 0.01/2 = 0.005

1- (alpha/2) = 1 - 0.005 = 0.995

Z critical value using z table for area 0.995 is 2.58

(0.084858, 0.215142) is the 99% confidence interval for the proportion of rotten apples in the orchard.