Question

Determine the minimum sample size required in order to estimate p, the population proportion, to within 0.05, with:

a) 95% confidence.

b) 99% confidence.

  

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 0.05

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 / 0.05)2 * 0.5* 0.5

= 384

Sample size = 384

B.

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 0.05

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 / 0.05)2 * 0.5 * 0.5

=665.64

Sample size = 666