Question

2)   A researcher wishes to be 95% confident that her estimate of the true proportion of

      individuals who travel overseas is within 2% of the true proportion. Find the sample

      size necessary if:

         a) No estimate of the sample proportion is available.

         b) In a prior study a sample of 190 individuals showed that 23 traveled overseas

               last year.

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.02

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.02)2 * 0.5 * 0.5

= 2401

sample size = n = 2401

b) Point estimate = sample proportion = = x / n = 23 / 190 = 0.121

1 - = 1 - 0.121 = 0.879

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

= (1.96 / 0.02 )2 * 0.121 * 0.879

= 1021.47

sample size = n = 1022