Question

For budgetary purposes, a manufacturing company needs to estimate the proportion of defective parts that a production process will create. What (minimum) sample size is needed to form a 98% confidence interval to estimate the true proportion of defective parts to within ± 0.04?

Do not round intermediate calculations. Round up your final answer to the next whole number.

Sample size =  parts

Answer 1

Solution :

Given that,

   = 1 - = 0.5

margin of error = E = 0.04

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z _0.01 = 2.326

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

= (2.326 / 0.04)² * 0.5 * 0.5

= 845

sample size = 845