Question

You wish to sample a population of voters in order to obtain a 99% confidence interval for the proportion of voters supporting Candidate A.

1. (10 points) If you wish the error term of your estimate to be less than 0.05, find the conservative number of voters that you will need to sample in order to accomplish this.

2. (10 points) Suppose now that your boss asks you to reduce this conservative error term by some factor k, where (0 < k < 1) what new sample size would be required? Suppose in particular the boss specifies that   k = 1/3, what would your new sample size have to be?

Answer 1

Ans:

a)For conservative case,we consider p=0.5

margin of error=0.05

z=2.58

Sample size required,n=2.58^2*0.5*(1-0.5)/0.05^2=665.64

n=666

b)As margin of error is inversely proportion to sqrt(n),so if we want to reduce it to one third i.e. k=1/3,then sample size will be 9 times.

So,new sample size,n=9*666=5994