Question

Determine the sample size n needed to construct a 99​% confidence interval to estimate the population proportion when p over bar equals 0.62 and the margin of error equals 7​%.

n=?????

Answer 1

Solution :

Given that,

= 0.62

1 - = 1 - 0.62 = 0.38

margin of error = E = 7% = 0.07

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 / 0.07)2 * 0.62 * 0.38

=320.05

Sample size = 321 rounded