Question

For a binomial experiment:

Find the sample size required to estimate the true proportion of Harvard Students that are in Accounting if you want the estimate to be within 0.09 with 99% confidence.

Round your answer up to the next larger integer, no matter how small the decimal.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =0.09

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.09)² * 0.5 * 0.5

=204.78

= 205

n = sample size = 205