10 The label on a particular size of milk carton states that it contains 1.5 litres of milk. In an investigation at the packaging plant the contents, \(x\) litres, of each of 60 randomly selected cartons are measured. The data are summarised as follows.
$$\Sigma x = 89.758 \quad \Sigma x ^ { 2 } = 134.280$$
- Estimate the variance of the underlying population.
- Find a 95\% confidence interval for the mean of the underlying population.
- What does the confidence interval which you have calculated suggest about the statement on the carton?
Each day for 300 days a random sample of 60 cartons is selected and for each sample a \(95 \%\) confidence interval is constructed.
- Explain why the confidence intervals will not be identical.
- What is the expected number of confidence intervals to contain the population mean?