Course Notes - Department of Mathematics and Statistics

As Fred wants to know the proportion within 3%, 3% is the maximumvalue the right hand side can take, also since we do not know whatproportion our new poll will give, we set p = to 0.5 as this gives us thewidest interval. So we need to rearrange the equation below to make nthe subject.√0.5(0.5)1.96 ×≤ 0.03√n0.5(0.5)≤ 0.03n1.960.5(0.5)≤ 0.0153 2n0.25 ≤ 0.000234 × n0.25≤ n0.0002341067.11 ≤ nSince n must be greater than or equal to the value we have found andFred cannot poll 0.11 of a person. Fred requires at minimum 1068people to be 95% confident of his result within 3%.Part IIAs he was getting into local body politics Fred thought he better loseabout 5 kg for all the photo opportunities. Ten of his friends had used aparticular diet. They helpfully gave Fred their initial weights and theirweights after completing the programme. These can be summarized inthe table below.116