Stat 5132 (Geyer) Old Final Exam Solutions

# Stat 5132 (Geyer) Old Final Exam Solutions - Up Stat 5132...

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Up: Stat 5132 Final Problem 1 The test statistic is Under the null hypothesis Z is standard normal. From Table I in Lindgren, the one-tailed P -value is 0.0537. Problem 2 Welch's procedure uses the test statistic Under the null hypothesis T has an approximate Student t -distribution with noninteger d. f. given by From Table IIIa in Lindgren, the one-tailed P -value is 0.041 and the two-tailed is (double that) 0.082. (The exact P -value using a computer is 0.081.) Problem 3 The test statistic

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has an asymptotic standard normal distribution under the null hypothesis .For an level upper-tail test, we reject when Z > 1.6449 (Table 1a in Lindgren). Under the alternative hypothesis is approximately standard normal. We don't know what S will be. In order to do a calculation we plug in the estimate from preliminary data ( S = 4). The power condition is where P A here means probability under the alternative (under which Z A is standard normal). From Table 1a in Lindgren we see that P A ( Z A > -1.2816) = 0.9 so we find
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Stat 5132 (Geyer) Old Final Exam Solutions - Up Stat 5132...

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