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Oct26_examples

# Oct26_examples - 10.22 The hardness of a certain rubber(in...

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October 26th Examples 10.13 The output voltage for a certain electric circuit is speciﬁed to be 130. A sample of 40 independent readings on the voltage for this circuit gave a sample mean of 128.6 and a standard deviation of 2.1. Test the hypothesis that the average output voltage is 130 against the alternative that it is less than 130. Use a 5% signiﬁcance level. 10.14 Refer to 13. If the voltage falls as low as 129, serious consequences may result. For testing H 0 : μ 130 vs. H a : μ = 129, ﬁnd β , the probability of a Type II error, for the rejection region used in exercise 13. 10.20 A manufacturer of resistors claims that 10% fail to meet the established tolerance limits. A random sample of resistance measurements for 60 such resistors reveals eight to lie outside the tolerance limits. Is there suﬃcient evidence to refute the manufacturer’s claim, at the 5% signiﬁcance level? Find the p-value for this test.
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Unformatted text preview: 10.22 The hardness of a certain rubber (in degrees Shore) is claimed to be 65. Fourteen specimens are tested, resulting in an average hardness measure of 63.1 and a standard deviation of 1.4. Is there suﬃcient evidence to reject the claim, at the 5% level of signiﬁcance? What assumption is necessary for your answer to be valid? 10.36 Aptitude tests should produce scores with a large amount of variation so that an administrator can distinguish between persons with low aptitude and persons with high aptitude. The standard test used by a certain industry has been producing scores with a standard deviation of 5 points. A new test is tried on 20 prospective employees and produces a sample standard deviation of 8 points. Are scores from the new test signiﬁcantly more variable than scores from the standard? Use α = 0 . 05 ....
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