1. Tutorial 10
The following data are the lives of 15 radio tubes selected at random from a large batch of tubes:
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:
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:
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