4 In a survey a random sample of 150 households in Nantville were asked to fill in a questionnaire about household budgeting.
- The results showed that 33 households owned more than one car. Find an approximate \(99 \%\) confidence interval for the proportion of all households in Nantville with more than one car. [4]
- The results also included the weekly expenditure on food, \(x\) dollars, of the households. These were summarised as follows.
$$n = 150 \quad \Sigma x = 19035 \quad \Sigma x ^ { 2 } = 4054716$$
Find unbiased estimates of the mean and variance of the weekly expenditure on food of all households in Nantville.
- The government has a list of all the households in Nantville numbered from 1 to 9526. Describe briefly how to use random numbers to select a sample of 150 households from this list.