A rasearcher wishes to estimate with 95 confidence the perce

A rasearcher wishes to estimate, with 95% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 5% of the true proportion a) Find the minimum sample we needed using a prior study that found that 24% of the respondents said they support abolishing the penny. b) No preliminary estimate is available. Find the minimum sample size needed. a) What is the minimum sample size needed using a prior study that found that 24% of the respondents said they support abolishing the penny? n= [ ] (Round up to the nearest whole number as needed ) b) What is the minimum sample we needed assuming that no poor information is available? n= [ ] (Round up to the neatest whole number as needed )

Solution

95% CI means z = 1.96

Given MOE = 0.05

a.) p = 0.24

s.d = sqrt(p*(1-p)/n)

MOE = z*s.d

0.05 = (1.96)*sqrt(0.24*0.76)/n)

So sqrt(n) = 16.74

So n = 280.28

So n = 281

b.) no prior information means p = 0.5

So 0.05 = (1.96)*sqrt(0.5*0.5/n)

So sqrt(n) = 19.6

So n = 384.16

So n = 385