Let us experiment to see how large n should be for the large-sample method confidence interval

for the mean of an exponential population to be accurate. Let (X1,X2, ... , Xn) be a random sample

from an exponential distribution with parameter . We can construct the confidence interval for

the population mean (=1/). Let us investigate the accuracy of this interval, i.e., how close its

estimated coverage probability is to the assumed nominal level of confidence, for various

combinations of (n, ). Let us also consider that = 0.05, = 0.01, 0.1, 1, 10 and n = 5, 10, 30,

50, 100. Thus, we have a total of 4 * 5 = 20 combinations of (n, ) to investigate.

(a) For a given setting, compute the estimates of coverage probability of the confidence

interval by simulating appropriate data, using this to construct the confidence interval, and

repeating the process 6000 times.

(b) Repeat (a) for the remaining combinations of (n, ). Present an appropriate summary of the

results.

(c) Give the interpretation of the results. Please answer the following questions also:

how large n is needed for the interval to be accurate? Does this answer depend on ?

(d) The conclusions in (c) depend on the specific values of that were fixed in advance or not.

Please explain.