Question

Determine the sample size n needed to construct a 90​% confidence interval to estimate the population proportion when p over bar equals 0.64 and the margin of error equals 7​%.

n=???

Answer 1

Solution :

Given that,

= 0.64

1 - = 1 - 0.64 = 0.36

margin of error = E = 7% = 0.07

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 / 0.07)2 * 0.64* 0.36

=127.2384

Sample size = 128