Consider the power calculation done in Example 9.5.5.
a. Simulate v0 = 1000 i.i.d. noncentral t pseudo-random variables with 14 degrees of freedom and noncentrality parameter 1.936.
b. Estimate the probability that a noncentral t random variable with 14 degrees of freedom and noncentrality parameter 1.936 is at least 1.761. Also, compute the simulation standard error.
c. Suppose that we want our estimator of the noncentral t probability in part (b) to be closer than 0.01 to the true value with probability 0.99. How many noncentral t random variables do we need to simulate?