Question

Find the sample size needed to estimate the percentage of Virginia residents who are left-handed. Use a Margin of Error of 3% and use a confidence level of 90% for both situations as follows.

a) Assume phat is unknown

b) Based on prior studies, use phat = 12%

Answer 1

Solution :

Given that,

a)

= 1 - = 0.5

margin of error = E = 0.03

Z/2 = 1.645

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

= (1.645 / 0.03)2 * 0.5 * 0.5

= 752

sample size = 752

b)

= 0.12

1 - = 1 - 0.12 = 0.88

margin of error = E = 0.88

Z/2 = 1.645

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

= (1.645 / 0.03)2 * 0.12 * 0.88

= 318

sample size = 318