Question

Step by step please

A researcher wishes to estimate with 95% confidence the proportion of people that own home computers. No previous study was available for a proportion estimate. The researcher wants to be accurate within 2% of the true proportion. How large of a sample is necessary?

*hint: when no proportion estimate is available, we use p-hat = .50

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

margin of error = E = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.02)² * 0.50 * 0.50

= 2401

sample size = 2401