Question

Determine the sample size n needed to construct a 90 ​% confidence interval to estimate the population proportion when p equals 0.39 and the margin of error equals 5 ​%.

n=___

Answer 1

Solution :

Given that,

= 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 5% = 0.05

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.65 ( Using z table)

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

= (1.65 / 0.05)2 * 0.39 * 0.61

=259

Sample size = 259