We are interested in conducting a study in order to determine what percentage of voters would...

We are interested in conducting a study in order to determine what percentage of voters would vote for the incumbent president. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.03 or less at 99% confidence?

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Expert Solution

Solution:

Given:

Margin of Error = E = 0.03

Confidence level = c = 99% = 0.99

We have to find sample size n.

Since p is unknown, we use p = 0.5

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 sample size n is:

orchestra answered 1 year ago

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