Following from Exercise 41.6, suppose Y Gamma(k = 24, = 1). a. What is E(Y)?

Following from Exercise 41.6, suppose Y ∼ Gamma(k =

24, λ = 1).

a. What is E(Y)?

b. Again we wish to test H0 : µ = 25. Compared with the simulation in Exercise 41.6, what do you expect to happen to the P-value for this test?

c. Simulate n = 10 observations fromY and test H0 using the t.test command. Do you get the results you expect?

d. What would you expect to happen to the P-value if you simulate n = 1000 observations from Y instead of n = 10?

Make a note of what you think will happen, then run the simulation in R and record your findings.

e. Explain why the P-value in part

(d) changed in the way it did.