A specialist in precision machinery wants to estimate the mean expansion of cert

Question

A specialist in precision machinery wants to estimate the mean expansion of certain pistons (in inches) on the basis of a sample of 42 of these pistons. The expansion is caused by the heat generated after the engines have been started, and it is known that sigma = 0.020 inch. If the specialist considers the data to constitute a random sample, what can he assert with probability 0.99 about the maximum error if he uses the mean of his sample as an estimate of the actual mean expansion of such pistons. A buyer for a large wholesaler of vegetables plans to estimate the mean weight of the Hubbard squash in a freight car load of these squash. To obtain this estimate the buyer will determine the weight of a gross (144) of the squash from this shipment. The buyer knows, from experience and from inspection, that the standard deviation is sigma = 3.00 pounds. What can the buyer assert, with probability 0.95, about the maximum error of the estimate? A mailing supervisor wants to use the mean of a random sample of the time it takes to prepare and address catalogs for mailing. If, based on experience, the supervisor can assume that sigma = 0.50 minutes for such data, what can he assert with probability 0.99 about the maximum size of the error?

Explanation / Answer

9.3) for std error =std deviation/(n)1/2 =0.003

for 99% CI, z=2.5758

hence maximum error =margin of error =z*Std error =0.0079

9.5)

for std error =std deviation/(n)1/2 =0.05

for 99% CI, z=2.5758

hence maximum error =margin of error =z*Std error =0.1288

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