Question

A person would like to create a 99% confidence interval for a particular unknown population proportion. They would like the interval to have a width no wider than 0.1 and do not yet have an estimate for the value of the unknown population proportion. How large of sample should they use in when creating this confidence interval?

Use at least 4 decimal places of accuracy in all values, including the z-score.

hint: your answer will reflect how many individuals will need to be included in the study so it should be an integer value. Non-integer values will be counted wrong.

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = width / 2 = 0.1 / 2 = 0.05

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.5758

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

= (2.5758 /0.05 )2 * 0.5 * 0.5

= 663.47

sample size = n = 664