Question

A manufacturer of cell phones wants to estimate the proportion of the defective phones the factory produces.

How many cell phones should be sampled and checked in order to estimate the proportion of the defective phones in the population to be within 4% margin of error with 99% confidence? [This is a sample size determination question for proportion. ]

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Sample size = n = ((Z / 2) / E)2 * * (1 - )

= (2.576 / 0.04)2 * 0.5 * 0.5

= 1037

n = sample size = 1037