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A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of synthetic diamonds is greater than 0.5 karat. To evaluate the profitability of the process, 38 synthetic diamonds are generated with a mean of 0.52 karat and a standard deviation of 0.0655 karat. Is there sufficient evidence to indicate that the average weight of synthetic diamonds produced by the new process is greater than 0.5 karat? Use α = 0
a) Define the parameter of interest and set up the hypotheses in terms of the parameter.
b) Briefly explain why the t statistic should be used in this case
c) Compute the value of the test statistic
d) What conclusion can we draw? use the p-value approach
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