Question

According to the American Academy of Opthalmology, 32% of Americans have blue eyes. Use the Standard Normal Probability and the Inverse Normal tables to answer the questions. (Answers should be to the nearest 0.1%)

1. With a sample size of 700, the middle 95% of samples will have sample proportions between  and  .
2. With a sample size of 1300, the middle 95% of samples will have sample proportions between  and  .
3. With a sample size of 1850, the middle 95% of samples will have sample proportions between  and  .

Answer 1

p=0.32

q=1-p

=1-0.32

=0.68

For 95% confidence,Zα/2 =1.96

a)

n=700

CI = p ± Zα/2 × √[(p×q)/n]

   = 0.32 ± 1.96 ± √[(0.32×0.68)/700]

   = 0.32 ± 0.034557

   = (0.285,0.355)

b)

n=1300

CI = p ± Zα/2 × √[(p×q)/n]

   = 0.32 ± 1.96 ± √[(0.32×0.68)/1300]

   = 0.32 ± 0.025357

   = (0.295,0.345)

c)

n=1850

CI = p ± Zα/2 × √[(p×q)/n]

   = 0.32 ± 1.96 ± √[(0.32×0.68)/1850]

   = 0.32 ± 0.021256

   = (0.299,0.341)