Question

Suppose you want to estimate the percentage of people who smoke, and you want your estimate to be within 3 percentage points of the correct population measure, based upon an 90% confidence level. What minimum size sample is required? Assume that no estimate of "p-hat" is known.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 05  

margin of error = E = 0.03

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 / 0.03)² * 0.5 * 0.5

= 751.67 = 752

sample size = 752