Milk cartons are advertised to contain one litre of milk. From a random sample of 18 one-litre cartons whose contents were accurately measured by the South African Bureau of Standards (SABS), it was found that the average fill was 0.981 l with a sample standard deviation of 0.052 l. Assume that the fill of one-litre milk cartons is normally distributed.

(a) Using a 99% confidence level, estimate the actual mean fill of all one-litre milk cartons. Interpret your findings and comment on the question: 'Do one-litre cartons of milk contain one litre of milk on average?'

(b) Repeat the exercise in (a) above, but use a 95% confidence level. Explain any differences in the conclusions.

(c) Compute the confidence intervals in (a) and (b) using Excel's TINV formula.