Suppose that a 99% confidence interval for the mean p, of a normal distribution is found to be (-2.0, 3.0). Would a test of H0: = —3 versus HA:  = —3 be rejected at the .01 significance level?

Let X be a binomial random variable with n trials and probability p of success.

a What is the generalized likelihood ratio for testing H0 : p = .5 versus HA: p  5?

b Show that the test rejects for large values of [X — n/2].

c Using the null distribution of X, show how the significance level corresponding to a rejection region [X — n/2] > k can be determined.

d If n = 10 and k = 2, what is the significance level of the test?

e Use the normal approximation to the binomial distribution to find the significance level if n = 100 and k = 10.

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