Question

A pilot sample of 75 items was taken, and the number of items with the attribute of interest was found to be 15. How many more items must be sampled to construct a 99% confidence interval estimate for p with a 0.025 margin of error

Answer 1

Solution :

Given that,

n = 75

x = 15

Point estimate = sample proportion = = x / n = 15 / 75 = 0.2

1 - = 1 - 0.2 = 0.8

margin of error = E = 0.025

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = 2.576

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

= (2.576 / 0.025)² * 0.2 * 0.8

= 1698.75

sample size = n = 1699