## EXAMPLES OF HYPOTHESIS TESTS

In the preceding sections we have studied the theory of hypothesis testing. In this section we shall apply it to various practical problems.

EXAMPLE 9.6.1 (mean of binomial) It is expected that a particular coin is biased in such a way that a head is more probable than a tail. We toss this coin ten times and a head comes up eight times. Should we conclude that the coin is biased at the 5% significance level (more precisely, size)? What if the significance level is 10%?

From the wording of the question we know we must put (9.6.1) H0: p = У2 and Яр p > У2.

From Example 9.4.2, we know that we should use X ~ B(10,p), the number of heads in ten tosses, as the test statistic, and the critical region should be of the form

(9.6.2) R = {c, c + 1, . . . , 10},

where c (the critical value) should...

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