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06egHTscd - ISOM111 Business Statistics(Fall 2010 Tutorial...

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ISOM111 Business Statistics (Fall 2010) Tutorial Exercise 6 Examples for Procedures of Testing Hypotheses about Population Mean μ X Solutions for [Part C] & [Part D] (Ci) Is there any evidence showing that the machine manufactures the cloth with a lower average breaking strength than the manufacturer’s speci fi cations at 5% signi fi cance level? State the null and H 0 : μ 70 pounds alternative hypotheses: H a : μ < 70 pounds State α : α = 0 . 05 Critical value: z α = 1 . 645 Decision Rule: Reject H 0 if z < 1 . 645 Test Statistics: z obs = X μ 0 σ/ n = 68 . 5 70 3 . 5 / 49 = 3 . 00 Decision: Since z obs = 3 . 00 < 1 . 645 , we reject H 0 at 5% level of signi fi cance. Conclusion: There is SUFFICIENT EVIDENCE to conclude that the machine manufactures the cloth with a lower average breaking strength than the manufacturer’s speci fi cations at 5% level of signi fi cance.
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(Cii) Is there any evidence showing that the machine deviates from the manufacturer’s speci fi cations for average breaking strength? ( α = 0 . 05) State the null and
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