06egHTsab

# 06egHTsab - 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 A] & [Part B] 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. (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 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 = 71 . 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.

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