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

only if the average weight of the diamonds produced by the process is greater than 0.5

karat. To evaluate the profitability of the process, a sample of six diamonds was

generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54

karat. Do the six measurements present sufficient evidence to indicate that the average

weight of the diamonds produced by the new process is in excess of 0.5 karat?