Question

Show all your calculations and write out all the assumptions you used to arrive at your answer. I will assume everyone is doing a random sampling (as opposed to stratified or another alternative sampling scheme).

According to the news article in the New York Times, 62% of voters in Phoenix, AZ voted to continue expanding the rail system. You wish to conduct a public opinion survey to see if this is really the case.

What is the sample size you will need to have an acceptable sample error of 2% with a 90% Confidence Interval (CI)? Also, we will assume the worst case of information and say our expected mean proportion of votes in favor of transit expansion is 50%.

Assume two levels of electorate: 150,000 and 4,500

Answer 1

Here we assume that the sampling distribution of the sample proportion is normally distributed.

Formula of sample size( n ) for proportion :

Let's find critical value Zc using excel

c = confidence level = 0.90

1 - c = = 0.10

/2 = 0.05

-Zc = "=NORMSINV(0.03)" = -1.645

Therefore Zc = 1.645

p = Assume proportion of voters in Phoenix, AZ voted to continue expanding the rail system = 0.62

E = margin of error = 0.02

Plugging these value in the formula of n, so we get :

n = 1593.85 =1594

Now let's find n in case of p = 0.5

n = 1691.27 = 1692 ( Because we round sample size to the next integer).