Solution to Problem 20 in Chap 10

# Solution to Problem 20 in Chap 10 - = 0.10 n×p = 6< 10...

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Solution to Problem 10.20 Problem 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 revel eight to lie outside the tolerance limits. Is there sufficient evidence to refute the manufacturer’s claim, at 5% significance level? [The last sentence in the text “Find p-value of the test.” is redundant. Why?] The solution Let p = the proportion of all resistors (produced by this manufacturer) that do not meet the established tolerance limits. The manufacturer’s claim is p = 0.10. If there is sufficient evidence to refute this claim, we will believe p > 0.10 [We will be happy if p < 0.10, why?] Hence the hypotheses of interest are Ho: p = 0.10 vs. Ha: p > 0.10. Assumptions: 1. SRS? Yes, the problem states so. 2. Categorical variable, with 2 categories? Yes, the resistors either meet the established tolerance limits or not. 3. Large Sample? Since n = 60 and p
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Unformatted text preview: = 0.10, n×p = 6 < 10. This condition is not satisfied hence we CANNOT use the normal approximation to the binomial distribution. However, we may use exact distribution. Hypotheses: Ho: p = 0.10 vs. Ha: p > 0.10. Test Statistic: is Y = Number of resistors in the sample that do not meet the established tolerance limits. Then Y ~ B(60, 0.10). [Why? Check all 5 conditions for the binomial distribution.] The p-value: Remember the general definition of the p-value: From the observed data we have, We can find the above probability using a more extensive table than what you have in your text [Table 2 in the appendix]. Alternatively, we can see and state that Decision: Reject Ho since the p-value is extremely large. Conclusion: The observed sample give strong evidence to indicate that the proportion of resistors that do not meet the established limits in the population exceeds the manufacturer’s claim of 10%....
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