No level of significance was given in the problem

No level of significance was given in the problem--can you think of an approach that doesn't involve a specific alpha level?

I need the above question answered to reply to my problem that you answered before which is posted below. 

I DO NOT need the below question answered, you already did that. I need the above question answered. 

(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? )