XCO, a multinational manufacturer, uses a batch process to produce widgets. Each batch of widgets takes 8 hours to produce and has material and labor costs of $8,476. Because of variations in machine efficiency and raw material purity, the number of widgets per batch is random. All widgets made can be sold for $2.50 each, and widget production is profitable so long as the batches sell for more than $12,500 on average. XCO sampled 16 batches and found 5,040 widgets per batch on average, with a standard deviation of 41.3 widgets. At α = 0.025, can XCO conclude that its widget operation is profitable?
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