1.26 A binomial sample of size n has y = 0 successes.

a. Show that the confidence interval for based on the likelihood function is

[0.0, 1 exp(-22/2/2n)]. For a = 0.05, use the expansion of an exponential function to show that this is approximately [0, 1.92/n].

b. For the score method, show that the confidence interval is [0, 22/2/(n + 2a/2)], or [0, 3.84/(n + 3.84)] when a = 0.05. (See Exercise 16.30 for small-sample intervals when y = 0.)