Question 343878: Question 5 (15 marks)
Marking criteria
Marks will be awarded for the correct inference technique and will include such aspects as appropriate detailed working, diagrams, correct calculations and conclusions, correct use of Excel.
a. Eleven percent of the products produced by an industrial process over the past several months fail to conform to the specifications. The company modifies the process in an attempt to reduce the number of non-conformities. In a trial run, the modified process produces 16 nonconforming items out of a total of 300 produced. Do these results demonstrate that the modification is effective? (Test at a = 0.01)
(8 marks)
b. Use the appropriate Excel macro from the set of workbooks Test Statistics.xls to verify your answer to Part a. Include the resulting Excel output. With reference to the appropriate cells show how the output provided verifies your answer to Part a.
(3 marks)
c. Find the p-value of the test from the output generated in Part b. Explain how this value can be used to test the hypothesis in Part a.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a. Eleven percent of the products produced by an industrial process over the past several months fail to conform to the specifications.
The company modifies the process in an attempt to reduce the number of non-conformities.
In a trial run, the modified process produces 16 nonconforming items out of a total of 300 produced. Do these results demonstrate that the modification is effective? (Test at a = 0.01)
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Ho: p = 0.11
Ha: p < 0.11
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p-hat = 16/300 = 0.0533
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Test Statistic: t(0.0533) = (0.0533-0.11)/sqrt[0.11*0.89/300] = -3.1369
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p-value: P(z<-3.1369) = 0.00085387..
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Conclusion: Since the p-value is less than 1%, reject Ho.
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Cheers,
Stan H.
(8 marks)
b. Use the appropriate Excel macro from the set of workbooks Test Statistics.xls to verify your answer to Part a. Include the resulting Excel output. With reference to the appropriate cells show how the output provided verifies your answer to Part a.
(3 marks)
c. Find the p-value of the test from the output generated in Part b. Explain how this value can be used to test the hypothesis in Part a.
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