6. (20pts) In a district containing 4000 houses the percentage of owned houses is to be estimated with a s.e. of not more than 2% and the percentage of two-car households with a s.e. of not more than 1%. (The figures 2 and 1% are the absolute values.) The true percentage of house owners is thought to lie between 45 and 65% and the percentage of two-car households between 5 and 10%. How large a sample is necessary to satisfy both aims? Give the true percentages of house owners and two-car households under which you obtain your estimate. Run a simulation with the sample size and percentages you give in the first question and verify that you achieve the desired precision approximately.