1. Tutorial 7
Consider the example discussed in the lecture, concerning the comparison of two teaching methods A and B, and let W denote the sum of the ranks of the children in group A.
(a). Find the critical region for a test of nominal size alpha=10%, for testing the hypothesis that the two methods are equally good (i) against the alternative that Method A is better
(ii) against the alternative that Method B is better
(iii) against the alternative that one method is better than the other.
(b). Give a complete tabulation of the distribution of W and calculate the mean and the variance of W.
(c ). Can you find the mean of W without actually working out its distribution?
(d). Can you find the variance of W without actually working out its distribution?
Find the median, the quartiles and the deciles of the following distributions:
(a). The Uniform distribution on the interval [10,30].
(b). The Exponential distribution with mean 20.
(c ). The Normal distribution with mean 10 and variance 4.
For a random sample of size n=5 from the Uniform distribution on the interval [0,2], find the density function of each of the order statistics of X1, X2, X3, X4 and X5.
1/15/2019
SA3202, Tutorial 7