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Unformatted text preview: October 28th Examples (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 pvalue for this test. Answer: H : p = 0 . 10 ,H a : p > . 10. Let X ∼ Bin ( n,p ) . p value = P ˆ P > 8 60 H true = P X n > 8 60 p = 0 . 10 = P ( X > 8  p = 0 . 10) = 1 P ( X ≤ 8  p = 0 . 10) = 1 8 X x =0 60 x (0 . 10) x (1 . 10) 60 x = 1 . 8583644 = 0 . 1416356 Note: You can find P ( X ≤ 8) where X ∼ Bin ( n = 60 ,p = 0 . 1) in R rather easily with pbinom(q=8, size=60, prob=0.10, lower.tail=TRUE) Now compare the p value to α to reject or not reject H . (10.20 remix) A manufacturer of resistors claims that 10% fail to meet the established tolerance limits. A random sample of resistance measurements for 150 such resistors reveals twenty to lie outside the tolerance limits. Is there sufficient evidence to refute thetwenty to lie outside the tolerance limits....
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 Fall '08
 Kyung
 Statistics, Standard Deviation, tolerance limits

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