Given X ~Binomial(n,p)

i) Derive the generalized likelihood ratio for testing

H0:p=0.5 vs. HA:p = 0.5

ii) Show that the test rejects for large values of X2n

iii) Using the distribution of X under H0 , show how the significance level corresponding to a rejection region

X2n >c

can be determined.

iv) If n=10 and c=2 , what is the significance level of the test?

v) Use the Normal approximation to the Binomial distribution to find the significance level if n=100 and c=10