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A new process for producing synthetic diamonds can be operated at a profitable level only if...

A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds is greater than 0.5 karat. Sixteen diamonds are generated, with a mean weight of 0.5457 karat and sample standard deviation equals 0.0552 karat. Assuming that the data is normal and using α =0.10, test if the data support the claim that the process is profitable.

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