Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 90% confident that you estimate is within 3.5% of the true population proportion. How large of a sample size is required?

Answer 1

SOLUTION:

From given data,

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 90% confident that you estimate is within 3.5% of the true population proportion. How large of a sample size is required?

Margin of error = E = 3.5% = 0.035

If prior estimate of population proportion does not exist then

= 0.5

90% confident

Critical value

90% = 90/100 = 0.90

= 1 - Confidence interval = 1-0.90 = 0.10

/2 = 0.10 / 2

= 0.05

Z_/2 = Z_0.05 = 1.645

Now consider the formula of Margin of error

E = Z_/2 * sqrt((1-) / n)

Squaring on both sides

E² =( Z_/2)² * ( (1-) / n)

n = (1-) * ( Z_/2 / E)²

n = 0.5(1-0.5) * ( 1.645 / 0.035)²

n =( 0.5*0.5 ) * (47)²​​​​​​​

n = 552.25

sample size = n 552