Tutorial 10 The following data are the lives of 15 radio tubes selected at random from a large batch of tubes: 67.1 46.9 59.2 63.7 78.5 63.3.

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Presentation transcript:

Tutorial 10 The following data are the lives of 15 radio tubes selected at random from a large batch of tubes: 67.1 46.9 59.2 63.7 78.5 63.3 67.7 47.2 59.9 64.1 56.8 63.4 73.3 49.1 63.2 Find a 90% CI for the upper quartile. What is the exact confidence coefficient associated with the interval? 2. A random sample of 10th-grade boys resulted in the following 20 observed weights: 142 134 98 119 131 103 154 122 93 137 86 119 161 144 158 165 81 117 128 103 Find a 90% CI for the median. What is the exact confidence coefficient? 3. An automobile manufacturer wishes to allow enough headroom in his automobiles to comfortably accommodate all but the tallest 5 percent of the people who drive. Former studies indicate that the 95th percentile was 70.3 inches. In order to see if the results of former studies are still valid, a random sample of size 100 was selected. It was found that the twelve tallest persons in the sample have the following heights: 72.6 70.0 71.3 70.5 70.8 76.0 70.1 72.5 71.1 70.6 71.9 72.8 What is a 95% CI for the 95th percentile of the distribution of the heights? Suppose that a random sample of size n is drawn from a population, and let Ri denote the rank of the i-th observation. Show that E(Ri)=(n+1)/2, Var(Ri)=(n^2-1)/12, Cov(Ri, Rj)=-(n+1)/12. Derive the mean and variance of Wilcoxon rank sum statistic Wa and Mann-Whitney statistic Ua. 1/17/2019 SA3202, Tutorial 10