A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of ounces ounces of coffee per cup. If it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain.
Believing that the mean amount of coffee dispensed by the machine, , is different from ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is ounces and that the standard deviation is ounces.
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