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06egHT-1 - higher than 71 5 pounds given the mean strength...

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ISOM111 Business Statistics (Fall 2010) Tutorial Exercise 6 Examples for Procedures of Testing Hypotheses about Population Mean μ X Suppose the director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s speci fi cations, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 71.5 pounds. [Part A] (Ai) Is there any evidence showing that the machine manufactures the cloth with a higher average breaking strength than the manufacturer’s speci fi cations at 5% signi fi cance level? State the null and alternative hypotheses: State α : Critical value: Decision Rule: Test Statistics: Decision: Conclusion: (Aii) Compute the probability of getting a sample mean strength of 49 pieces of cloth that is
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Unformatted text preview: higher than 71 . 5 pounds given the mean strength of cloth is 70 pounds . It is what we called as ____________________ [Part B] (Bi) Is there any evidence showing that the machine deviates from the manufacturer’s speci f cations for average breaking strength? ( α = 0 . 05) (Bii) Compute the corresponding p-value [Part C] If the sample mean of 49 pieces of cloth is 68.5 pounds. (Ci) Is there any evidence showing that the machine manufactures the cloth with a lower average breaking strength than the manufacturer’s speci f cations at 5% signi f cance level? (Cii) Is there any evidence showing that the machine deviates from the manufacturer’s speci f cations for average breaking strength? ( α = 0 . 05) (Ciii) Report the p-values for (i) and (ii). [Part D] Redo Part C (i)-(iii) if the sample mean of 49 pieces of cloth is 69.1 pounds....
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