A company, Marathon Products, has purchased a large quantity of steel wire from Gate and Fence (Pty) Ltd. The supplier, Gate and Fence (Pty) Ltd, claims that the wire has a mean tensile strength (i.e. breaking strength) of more than 80 kg. Marathon Products will only accept the consignment of wire if this claim can be supported. Their quality controller sampled 26 pieces of this wire and found that the sample mean tensile strength was 81.3 kg with a standard deviation of 3.6 kg. Assume that tensile strength is approximately normally distributed.
Should Marathon Products accept this steel wire consignment?
(a) Conduct a hypothesis test for a single mean at the 5% significant level and advise the management of Marathon Products accordingly. Show the null and alternative hypothesis for this test.
(b) Compute the p-value for this test using Excel's TDIST function, and interpret the findings in the management context.