Mean or a proportion ? and solve problem accordingly

Question

1. Find the sample size needed to estimate the percentage of republicans among registered voters in California. Use a 0.03 margin of error; use a confidence level of 90%.

Answer 1

We need to analyze the margin of error and make sure it is less than 3%

 

The margin of error for a 90% CI for a proportion would be 

 

1.645sqrt(p(1-p)/n)

 

Although I am not given p, we can use .5 because .5 will give the largest standard deviation for a fixed value of n.

Therefore, no matter what p is once a sample is selected the margin of error will be controlled

 

1.645sqrt(.5*.5/n) < .03

 

sqrt(.25/n)<.03/1.645

 

.25/n < (.03/1.645)^2

 

1/n < 4(.03/1.645)^2

 

n > 1/(4(.03/1.645)^2) = 751.67

 

A sample size of at least 752 will be needed if you want to control the margin of error to be within 3%