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Unformatted text preview: STAT 350 Homework #8 ch8: 4,6,12,15,16,19,20,22,26,29 4. Let denote the population standard deviation of sheath thickness. The relevant hypotheses are: 05 . : 05 . : a H versus H This is because the company is interested in obtaining conclusive evidence that 05 . . A Type I error would be: concluding that the true standard deviation of sheath thickness is less than .05mm when, in fact, it is not. 6. Let denote the true average compressive strength of the mixture. The relevant hypotheses are: 300 , 1 : 300 , 1 : a H versus H A Type I error would be: concluding that the mixture meets the strength specifications when, in fact, it does not. A Type II error would be: concluding that the mixture does not meet the strength specifications when, in fact, it does. 12. (a) 87 . 2 50 06 . 1 34 43 . 34 z So, pvalue = 2P(z > 2.87) = 2(.0021) = .0042 [Note: Since H a is a twotailed test, the pvalue is the sum of the area in the two tails. That is, pvalue = P(z < 2.87) + P(z > 2.87) = 2P(z > 2.87)] (b) 87 . 2 50 06 . 1 34 57 . 33 z So, pvalue = 2P(z < 2.87) = 2(.0021) = .0042 (c) 24 . 2 32 89 . 1 34 25 . 33 z So, pvalue = 2P(z < 2.24) = 2(.0125) = .025 (d) 57 . 1 36 53 . 2 34 66 . 33 z So, pvalue = 2P(z > 1.57) = 2(.0582) = .1164 15. Let denote the true average speedometer reading (at 55 mph). Since we are concerned about whether the speedometer readings may be too high or too low (compared to 55 mph), this requires a 2sided test...
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 Spring '08
 Staff
 Statistics, Standard Deviation, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, Douglas fir, 05mm

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