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?

[edit]Download Attachments:

Part one: 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?

• 1.State the hypothesis, and identify the claim. 2. Find the critical values. 3. Compute the test value. 4. Make the decision. 5. Summarize the results.

Part two: Suppose that your sample size jumps to n = 60, and that allows us to assume that the sample is normally distributed. What is the corresponding P-value? At the alpha level of 0.05, would the p-value you get mean that you reject or fail to reject the null hypothesis?