Question

3 4) Suppose you wish to determine the proportion of college students in your state who receive some form of financial aid. You want to be 98% confident of your results and have a maximum error of 5%. Calculate the minimum sample size needed to meet these requirements given that the financial aid office at a local institution estimates the percentage to be 78%. I

Answer 1

We know that 98% confidence interval for true proportion is given by:

p(1-P) (p = 20.02/21 n

We want to find 'n' such that

p(1-P) 20.02/2V < 0.05 n p(1-P) 20.01 V < 0.05 n 0.78(1 -0.78) (2.3263) < 0.05 n n> 371.45714

So, minimum sample size = 372