Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within

4

percentage points with

95​%

confidence if​(a) he uses a previous estimate of

26%?

​(b) he does not use any prior​ estimates?

​(a)

nequals=nothing

​(Round up to the nearest​ integer.)​(b)

nequals=nothing

​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 0.26

1 - = 1 - 0.26 = 0.74

margin of error = E =4 % = 0.04

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 ( Using z table )

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

= (1.96 / 0.04)2 * 0.26 * 0.74

= 461.9524

Sample size =462

(B)

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =4 % = 0.04

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 ( Using z table )

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

= (1.96 / 0.04)2 * 0.5* 0.5

= 600.25

Sample size =601