Question

Find the minimum sample size required to estimate a population proportion with a margin of error equal to .04 and a confidence level of 90%. A recent study resulted in a sample proportion of .70. Also determine the minimum sample size if no prior study was done.

Answer 1

Solution :

Given that,

= 0.70

1 - = 1 - 0.70= 0.3

margin of error = E = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.04)2 * 0.70 * 0.30

=355.165

Sample size = 356 rounded

part b

determine the minimum sample size if no prior study was done.

= 0.5

1 - = 0.5

margin of error = E = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.04)2 * 0.5* 0.5

=423

Sample size = 423 rounded