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Hypothesis Testing for the Average Weight of Diamonds Produced by a New Process

Hypothesis testing for diamond weight.

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    Hypothesis Testing for the Average Weight of Diamonds Produced by a New Process 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 in our textbook and utilized in the solutions to the Chapter 8 review problems Step 1 State the hypotheses and identify the claim. Step 2 Find the critical value(s) from the appropriate table in Appendix C. Step 3 Compute the test value. Step 4 Make the decision to reject or not reject the null hypothesis. Step 5 Summarize the results. Given data is, 0.46 , 0.61 , 0.52 , 0.48 , 0.57 , 0.54 n 6 x 0.53 s 0.0559 df n 1 6 1 5         1. STATING THE RESEARCH QUESTION. Is the mean weight of diamond = 0.5 karat The population of interest is all diamond that processed . The parameter of interest is the mean and the variable diamond weight is continuous. The hypothesized value of the parameter, the mean, is 0.5 karat . Since the parameter is a population mean of a continuous variable, this suggests a one sample test of a mean. 2. SPECIFY THE NULL AND ALTERNATIVE HYPOTHESES. The null hypothesis is the population parameter, μ = 0.5 (H 0 : μ = 0.5 ). The alternative hypothesis is the population parameter > 0 .5 ( H A : > 0 .5 ). This H A s uggests a one - tailed test . The next is to select a si gnificance level (Type I error), we take  is equal to 0 .05 level. Example: H 0 : μ = 0 .5 H A : μ > 0 .5  = 0 .05 Test assumptions are

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