Question

Leading up to each Federal Election, the various opinion pollsters conduct nation-wide surveys of electors in an attempt to forecast the proportion of the electorate who will vote for each of the major parties. Suppose that a polling firm conducts a survey of 500 randomly selected electors (a representative sample), and their results indicate that 210 of these electors will vote for the ALP at the election.
a. What is the point estimate of the proportion that will vote for the ALP?
b. Construct a 95% Confidence Interval for the (true) proportion of voters who will vote for the ALP at the election.
c. The polling firm wishes to be 95% confident that they have estimated the proportion who will vote for the ALP to within ±2% of the true value. What sized sample will be required to achieve this? [You may assume that the population proportion is estimated to be approximately 40%.]

Answer 1

solution:-

given that n = 500 , x = 210

a. point estimate p = x/n = 210/500 = 0.42

b. confidence interval

the value of 95% confidence from z table is 1.96

confidence interval formula

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.42 +/- 1.96 * sqrt(0.42 * (1-0.42)/500)

=> (0.377 , 0.463)

c. here given that margin of error E = 0.02

the value of 95% confidence from z table is 1.96

and p = 0.40

sample size formula

=> n = p * (1-p) * (z/E)^2

=> n = 0.40 * (1-0.40) * (1.96/0.02)^2

=> n = 2305