Question 3 Estimating population proportion [12 marks] Part 1: In 2009 Queensland suffered the worst floods in recent history. It caused disruption to not only the Queensland businesses but also business nationally. The survey, which was conducted among 2000 medium or large businesses with more than 100 employees nationwide, found that 15 per cent of businesses had experienced some disruption or closed. The data with 1 (affected) and 0 (not affected) were recorded.

a) Estimate with 95% confidence the proportion of all nation-wide businesses that experienced disruption or closure due to the floods. (5 marks)

b) Assume there are 500,000 small or large businesses in Queensland, what is the maximum number of businesses in Queensland that are affected by the flood. (2 marks)

Part 2: Determining the sample size for estimating population proportion.

Suppose we want to estimate the proportion of customers who prefer our company's brand to within 0.03 with 95% confidence. Find the sample size needed to guarantee that this requirement is met. You can use either method 1 or method 2. (5 marks)