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

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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? To answer this question conduct an appropriate test of hypothesis using the five step process outlined below.

Five Steps of Hypothesis Testing
1. Write the null hypothesis (H0).
2. Write the alternative hypothesis (H1).
3. Set alpha level (amount of error allowed) and determine degrees of freedom.
4. Pick & calculate the significance test that fits your design.
5. Decision Step: Accept or Reject the null.