business statistics

Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 4% margin of error at a 90% confidence level, what size of sample is needed?

Give your answer in whole people.

Answer 1

Hi Salma,

Formula for this is:

n=(z_alpha/2 /e)²(p(1-p)

Let’s break this down.

n=sample size, what we are looking for

z_alpha/2=

z-critical value for [(1-confidence level)/2]

Confidence level here is 90%, so 1-(confidence level)=10% or 0.1. 0.1/2=0.05.

z_0.05=1.645

That value is worth memorizing in most introductory statistics classes.

e=margin of error

p=probability of success

1-p=probability of failure

Note that “success” can be defined however we want. In this case, success implies that people vote for, instead of against, our candidate.

So, for our problem:

z_alpha/2=1.645

e=0.04

When we are not given a value for probability of success, we can assume that it is effectively a coin flip. That is:

p=0.5

So:

p=0.5

1-p=0.5

Therefore:

n=(1.645/0.04)²(0.5)(1-0.5)

n=422.81

Rounding to the next whole person:

n=423

I hope this helps.