Question

What sample size is needed to estimate the population proportion within 1 percent using a 99 percent confidence level?

Answer 1

Solution:

Given:

E = Margin of Error = 1% = 0.01

c = Confidence level = 99% = 0.99

p = estimate of proportion , which is unknown , thus we use p = 0.5

We have to find sample size n.

Formula:

Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Thus required sample size is: