Question

In a sample of 331 Americans, 48% decided to not go to college because they cannot afford it.

(b) Suppose we wanted the margin of error for the 90% confidence level to be at most 1.5%. How large of a survey would you recommend?(Do not use the estimate of p given by the sample.)

(c) Suppose we wanted the margin of error for the 90% confidence level to be at most 1.5%. How large of a survey would you recommend? (Now make the estimate that p ≈ 0.48)

Answer 1

(b)

If we do not have any estimate of p, we will assume p = 0.5 for the conservative value of sample size. This is because the sample size is largest for the p = 0.5 at a given margin of error.

z value for 90% confidence level is 1.645

Margin of error, E = 1.5% = 0.015

Sample size, n = =

= 3007 (Rounded to nearest integer)

We recommend survey with sample size of 3007

(c)

For p = 0.48

Sample size, n = =

= 3002 (Rounded to nearest integer)

We recommend survey with sample size of 3002.