Question

-You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required?

n =


Do not round mid-calculation. However, use a critical value accurate to three decimal places.

-You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=62%p∗=62%. You would like to be 99% confident that your esimate is within 0.1% of the true population proportion. How large of a sample size is required?

n =


Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Answer 1

Solution,

Given that,

1) =  1 - = 0.5

margin of error = E = 0.025

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.645 / 0.025 )² * 0.5 * 0.5

= 1082.41

sample size = n = 1083

2) = 0.62

1 - = 1 - 0.62 = 0.38

margin of error = E = 0.001

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.001 )² * 0.62 * 0.38

= 1563388.83

sample size = n = 1,563,389