Question

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 99​% confidence if

​a) she uses a previous estimate of 0.54​?

​b) she does not use any prior​ estimates?

Answer 1

Solution :

Given that,

a)

= 0.54

1 - = 1 - 0.54 = 0.46

margin of error = E = 0.05

  Z/2 = 2.576

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

= (2.576 / 0.05)2 * 0.54 * 0.46

= 659

sample size = 659

b)

= 1 - = 0.5

margin of error = E = 0.05

Z/2 = 2.576

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

= (2.576 / 0.05)2 * 0.5 * 0.5

= 664

sample size = 664