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hw8sol - Engineering 0020 Probability and Statistics...

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Engineering 0020: Probability and Statistics 1 (Spring, 2007) Solutions - Homework #8 2. a Complies; upper tail test. b Need to state alternative as H a : σ < 20. c Need to reverse the statements for H o and H a . d Need to restate the hypothesis so that the same value is applied in both H o and H a . e Hypothesis should be based on population parameter: σ 2 , not sample statistic S 2 . f Need to restate the hypothesis so that the same value is applied in both H o & H a . Also, H a should be stated as <, >, or . g Complies; two tailed test. h Complies; lower tail test. 4. When the alternative is H a : μ < 5, it means that the alternative hypothesis is that the water is safe . Thus the null hypothesis H 0 is that the water is unsafe , and we will reject H o only when there is strong evidence that it is false. Here, a type I error (i.e., we reject H o when it is true) means we conclude that the water is safe when it is actually unsafe. On the other hand, a type II error means we conclude that the water is unsafe when it is actually safe (i.e., we fail to reject H 0 when it is false). Clearly, a Type I error is much more serious. When the alternative is H a : μ > 5, it means that the alternative hypothesis is that the water is unsafe . Thus the null hypothesis H 0 is that the water is safe , and we will reject H o only when there is strong evidence that it is false.
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