Suppose that in a sequence of n Bernoulli trials, the probability p of success on each trial is unknown. Suppose also that p0 is a given number in the interval (0, 1), and it is desired to test the following hypotheses: H0: p = p0,
H1: p = p0.
Let Xn denote the proportion of successes in the n trials, and suppose that the given hypotheses are to be tested by using a χ2 test of goodness-of-fit.

Required:
Show that the statistic Q can be written in the form:

Q= n(Xn- po)^2/ po(1-po)