Question 3 (12 marks)

A national Australian banking corporation offering services both online and through traditional branches is interested in the extent that its customers are satisfied with its services. Management accordingly hires a research firm to estimate the proportion of its Australian customers that are satisfied with the bank's services. The research firm duly advised that 48 of a random sample of 400 of its customers indicated that they were satisfied.

a) Based upon this sample, name and give the value of the statistic that would be management's best estimate (or a point estimate) for the proportion of the bank's customers who are satisfied. (2 mark)

b) Use the Excel Estimators Macro to determine a 95% confidence interval for the proportion of the bank's Australian customers that are satisfied. Show that the assumption/s underlying the method used are satisfied. (5 mark)

c)What would need to be done to get an estimate of the required population proportion that has 95% probability of being within 1 percentage point of the true value. (1 mark)

Subsequently management finds that the research firm had in fact surveyed people (at random) as they exited a large Melbourne branch of their bank late on a Friday afternoon.

d. Comment briefly (using relevant statistical terminology) on:

i. the validity of the approach used and any implications for this inference; and

ii. whether conducting a larger survey in this same manner would likely lead to

more reliable inferences. (4 marks)