3.1.Milk cartons are advertised to contain one litre of milk. From a randomly 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 0.98 litres with a sample standard deviation of 0.052 litres. Assume that the fill of one-litre milk cartons is normally distributed

i. Using a 99% confidence level, estimate the actual mean fill of all one-litre milk cartons. Interpret your findings and comment on the question. (4)

ii. Repeat the exercise in (i) above, but use 90% confidence level. (4)

iii. Explain any differences in the findings computed above. (2)

3.2.A random sample of 300 Status cheque accounts at Capital Bank showed that 48 were overdrawn. When 250 Elite cheque accounts at the same bank were randomly checked, it was found that 55 were overdrawn.

Can the bank manager conclude that more Elite cheque account clients, proportionately, are likely to be overdrawn than Status cheque account clients? Test this hypothesis at the 4% level of significance. What conclusion can be drawn? (10)

3.3.To test claims statistically, sample data is gathered and analysed. On the basis of the sample findings, the hypothesised (or claimed) value of the population parameter is either accepted as probably true or rejected as probably false. This statistical process of testing the validity of a claim about the true value of any population parameter is known as hypothesis testing.

Enumerate on the steps followed by researchers when carrying out hypothesis testing. (10)