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 99​% confidence if

he uses a previous estimate of 38%?

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

Answer 1

Solution :

Given that,

= 0.38

1 - = 1 - 0.38 = 0.62

margin of error = E = 4% = 0.04

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

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

= (2.58 / 0.04)2 * 0.38 * 0.62

=980.15

n=980

(B)

Solution :

Given that,

= 0.5 ( assume )

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

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

= (2.58 / 0.04)2 * 0.5 * 0.5

=1040.06

n=1040