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409Quiz1ans - are met Suppose Metaltech decided to use a 5...

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STAT 409 Fall 2009 Name ANSWERS . Quiz 1 (3 points) Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Metaltech Industries manufactures carbide drill tips used in drilling oil wells. The life of a carbide drill tip is measured by how many feet can be drilled before the tip wears out. Metaltech claims that under typical drilling conditions, the life of a carbide tip follows a normal distribution. Suppose that certain regulations require the variance of the lifetimes to be no more than 12 feet 2 . Metaltech examines a random sample of 25 carbide tips to test whether these regulations
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Unformatted text preview: are met. Suppose Metaltech decided to use a 5% level of significance and the observed sample mean is 30.5 feet with the sample variance 16 feet 2 . Perform the appropriate test. Claim: σ 2 ≤ 12 H : σ 2 ≤ 12 vs. H 1 : σ 2 > 12 s 2 = 16. n = 25. Test Statistic: ( 29 ( 29 12 16 1 25 1 2 2 2 s ⋅ σ ⋅ χ-=-= n = 32 . Rejection Region: Right – tailed. Reject H if 2 2 α χ χ n – 1 = 24 degrees of freedom. α = 0.05 2 05 . χ = 36.42 . Reject H if 2 χ > 36.42. The value of the test statistic does not fall into the Rejection Region. Do NOT Reject H at α = 0.05 ....
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