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Discussion11%20Solutions - IE 300 GE 331 Discussion Problem...

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IE 300 / GE 331 Discussion Problem Set 11 8-10 𝑛𝑛 = 10, 𝑥𝑥̅ = 1.5045, 𝜎𝜎 = 0.01, 𝑧𝑧 0.005 = 2.58 The 99% confidence interval on the mean hole diameter is 𝑥𝑥̅ − 𝑧𝑧 0.005 𝜎𝜎 √𝑛𝑛 ≤ 𝜇𝜇 ≤ 𝑥𝑥̅ + 𝑧𝑧 0.005 𝜎𝜎 √𝑛𝑛 1.4963 ≤ 𝜇𝜇 ≤ 1.5127. 8-22 a) 𝑡𝑡 0.05,14 = 1.761 b) 𝑡𝑡 0.01,19 = 2.539 c) 𝑡𝑡 0.001,24 = 3.467 8-32 a) The data appear to be approximately normally distributed based on the q-q plot below which exhibits a reasonably straight line. b) 𝑛𝑛 = 6, 𝑥𝑥̅ = 16.98, 𝑠𝑠 = 0.319, 𝑡𝑡 0.005,5 = 4.032 Note that we should use the t-distribution since the data appear to be approximately normal, variance of the population is unknown, and the sample size is small. The 99% confidence interval on the mean is
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IE 300 / GE 331 Discussion Problem Set 11 𝑥𝑥̅ − 𝑡𝑡 0.005,5 𝑠𝑠 √𝑛𝑛 ≤ 𝜇𝜇 ≤ 𝑥𝑥̅ + 𝑡𝑡 0.005,5 𝑠𝑠 √𝑛𝑛 16.455 ≤ 𝜇𝜇 ≤ 17.505. We are 99% confident (NOT PROBABILITY) that the true mean lies within this interval.
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