Question

A sociologist wishes to estimate the proportion of parents of college-bound high school students who have not saved any money for college. What sample size would she need for the estimate to be correct within 6 percentage points with 95% confidence
(a) if she uses a similar study from 2015 that indicates that 32% of parents had saved no money for college?
(b) if she does not use any prior estimates?

Answer 1

Solution :

Given that,

= 0.32

1 - = 1 - 0.32= 0.68

margin of error = E = 6% = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.06)2 * 0.32 * 0.68

= 232.20

Sample size =232

b

Solution :

Given that,

= 0.5

1 - =0.5

margin of error = E = 6% = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.06)2 * 0.5 * 0.5

= 266.77

Sample size =267