Question

1. 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 95% confident that you estimate is within 1% of the true population proportion. How large of a sample size is required?

n =

2.Based on historical data in Oxnard college, we believe that 38% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to estimate the proportiton of freshmen who do not visit their counselors regularly. You would like to be 99% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

n =

3. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 26%. You would like to be 95% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

n =

Answer 1

Solution,

Given that,

1) =  1 - = 0.5

margin of error = E = 0.01

Z_/2 = Z_0.025 = 1.96   

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

= (1.96 / 0.01)² * 0.5 * 0.5

= 9604

sample size = n = 9604

2) = 0.38

1 - = 1 - 0.38 = 0.62

margin of error = E = 0.025

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.025)² * 0.38 * 0.62

= 2501.42

sample size = n = 2502

3) = 0.26  

1 - = 1 - 0.26 = 0.74

margin of error = E = 0.03

Z_/2 = Z_0.025 = 1.96   

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

= (1.96 / 0.03)² * 0.26 * 0.74

= 821.24

sample size = n = 822