Population Difference

Question 1 – 2017 Exam One Question 4 [20 marks]
When some companies run out of storage room at their premises, they hire off-site storage. When an item is required, they put in an online order, and the box is delivered to the office, usually the next working day (but not always).
One company has boxes stored at two different off-site storage locations.
(a) We wish to estimate the difference in population proportions delivered within a day from the two sites, using a 95% confidence interval. Assuming we will have equal sample sizes (n) from each site, what minimum n is needed such that the margin of error of the confidence interval is no more than 0.10? Note: we will have to assume the maximum standard error possible, which occurs when both  1 and  2 are 0.5.

(b) Over a three month period, the delivery times were noted as being one working day or less or two or more working days. The results were:

•  70 boxes came from site 1, and 57 were delivered within one working day;
•  64 boxes came from site 2, and 45 were delivered within one working day;
  Apply a formal statistical procedure at a 5% level to test of the population proportions of boxes delivered within one working day are the same for the two off-site locations.

Question 2 – 2017 Exam One Question 8 [20 marks]
A consumer group wanted to investigate whether two different removalist companies (labeled A and B) had the same or different price structures. They documented four office relocations of interest, and obtained quotes for each of these from the two companies. The quoted costs are summarised in the table below: