## TESTS OF HYPOTHESES

10.3.1 Student’s t Test

In Section 9.5 we showed that a hypothesis on the mean of a nomral i. i.d. sample with an unknown variance can be tested using the Student’s t statistic. A similar test can be devised for testing hypotheses on a and (3 in the bivariate regession model. Throughout this section we assume that ut) are normally distributed.

We shall consider the null hypothesis H0: (3 = (30, where (30 is a known specified value. A hypothesis on a can be similarly dealt with. Since (3 is a good estimator of p, it is reasonable to expect that a test statistic which essentially depends on (3 is also a good one. A linear combination of normal random variables is normally distributed by Theorem 5.3.2, so we see from (10.2.19) that

(10.3.1) ^Z(– (P – Po) ~ N(0, 1)

cr

2

under the null hypoth...

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