Question

A gigantic warehouse stores approximately

80 million empty aluminum beer and soda cans.​ Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with​ blackspot, rendering them unusable. A statistician was hired by the insurance company to estimate​ p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within 0.04 with 90​% confidence?

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.04

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.645 / 0.04)² * 0.5 * 0.5

= 422.82

sample size = 423