A data file contains randomly generated numbers. The column labeled X contains 35 numbers each generated with the following Excel command:

NORM.INV(RAND(); X; X);

A simulation exercise: Suppose that an analyst named Fred does not know X, X,

Y , or Y , but in one trial of an experiment is able to sample X and Y a total of 35

times each. Assume that X = Y , and that Fred somehow knows that these quantities

are equal, but Fred does not know the value of = X = Y . Fred wants to test

whether X > Y and his null hypothesis is H0 : X Y . The level of significance

is :05. Show simulation of this experiment: Suppose that you actually know that

X = 97, Y = 101, and = 40 (but Fred does not know this). Simulate only 1 trial

of the experiment (using Excel). For the one trial, (i) determine Fred's test statistic,

(ii) determine the p-value, and (iii) indicate whether Fred's null hypothesis is rejected.

[Note: With only one trial, you do not have to use a Data Table.]

e) For the given parameters and Fred's null hypothesis in part (d), (i) what is the probability of a Type I error and (ii) what is the probability of a Type II error?