Question

The 99% confidence interval for a population proportion is [0.645, 0.737]. Find the standard error involved in this confidence interval. (Z_{a/2}Za/2​ = 2.58). Please show how you arrive at your answer so I can understand how to calculate this. If you know the excel commands, that would be helpful as well.

Answer 1

Solution :

Given that,

Lower confidence interval = 0.645

Upper confidence interval = 0.737

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

= (0.645 + 0.737) / 2

= 1.382 / 2

= 0.691

1 - = 1 - 0.691 = 0.309

Margin of error = E = Upper confidence interval - = 0.737 - 0.691 = 0.046

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

0.046 = 2.58 * 0.691 * 0.309 / n

n = 25.91 = 672

standard error =  (( * (1 - )) / n) =  0.691 * 0.309 / 672 = 0.018