The Port and Customs authorities at Cape Town harbour claim that imported textile consignments are cleared within an average of 72 hours of the goods being offloaded from a vessel. A local textile importer is not convinced of this, and believes that the average clearance time is much longer. He analysed documents of 46 recent consignments and found that the average clearance time was 75.9 hours. Assume a population standard deviation of 18 hours and that clearance time is approximately normally distributed. Are the harbour authorities working to their stated clearance times?
(a) Formulate a suitable null and alternative hypothesis for this test situation.
(b) Test whether the local importer's claim is justified using a hypothesis test for a single mean. Use α = 0.10. What conclusion can be drawn?
(c) Compute the p-value for this test using Excel's NORMSDIST function and draw the appropriate management conclusion.