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

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