Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4 percentage points with 95​% confidence if ​(a) he uses a previous estimate of 32​%? ​(b) he does not use any prior​ estimates?

Answer 1

Answer:

sample size if he uses a previous estimate of 32​% is 523

sample size if he does not use any prior​ estimates is 601

Step-by-step explanation:

estimate E = 4 percentage = 0.04

confidence Cl = 95% = 0.95

previous estimate p = 32% = 0.32

q = 1 - 0.32 = 0.68

to find out

size of sample

solution

first we calculate z value for 95% confidence E = 0.04 is 1.96

from probability P(-1.96 < z < 1.96) = 0.95)

here z = 1.96

so in 1st part size of sample we know

E = z × $\sqrt{pq/n}$

put all value E, z p and q and we get n

n = (z/E)² ×p×q

n = (1.96/0.04)² ×0.32×0.68

n = 523

sample size if he uses a previous estimate of 32​% is 523

now in 2nd part we take p = 0.5

so n will be

n = (z/E)² ×p×q

n = (1.96/0.04)² ×0.5×0.5

n = 601

sample size if he does not use any prior​ estimates is 601