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

Hypothesis testing for diamond weight.

Chloe Martinez
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Hypothesis Testing for the Average Weight of Diamonds Produced by a NewProcessA new process for producing synthetic diamonds can be operated at a profitable level only if the averageweight of the diamonds produced by the process is greater than 0.5karat. To evaluate the profitability of theprocess, 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 averageweight of the diamonds produced by the new process is in excess of 0.5 karat? To answer this questionconduct an appropriate test of hypothesis using the five step process outlined in our textbook and utilized inthe solutions to the Chapter 8 review problemsStep 1State the hypotheses and identify the claim.Step 2Find the critical value(s) from the appropriate table in Appendix C.Step 3Compute the test value.Step 4Make the decision to reject or not reject the null hypothesis.Step 5Summarize the results.Given data is,0.46 , 0.61 , 0.52 , 0.48 , 0.57 , 0.54n6x0.53s0.0559dfn16151. STATING THE RESEARCH QUESTION.Is themean weight of diamond=0.5 karatThe population of interest is alldiamond that processed.The parameter of interest is the mean and the variablediamond weightis continuous.The hypothesized value of the parameter, the mean, is0.5 karat.Since the parameter is a population mean of a continuous variable, this suggests a one sample test of amean.2. SPECIFY THE NULL AND ALTERNATIVE HYPOTHESES.The null hypothesisis the population parameter, μ =0.5(H0: μ =0.5). The alternative hypothesis is thepopulation parameter>0.5( HA:>0.5). This HAsuggests aone-tailed test.The nextisto select a significance level (Type I error), we takeisequal to0.05 level.Example:H0: μ =0.5HA: μ>0.5=0.05Test assumptions are

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Statistics

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