Example 3

EXAMPLE 3 Identifying valid and invalid hypotheses

Determine whether the following hypotheses are in a valid form or not. If not, explain why not, and put the hypotheses in a valid form.

Solution

Invalid. The equal sign always goes in $H_{0}$ . So the correct form is:

$H_{0} : μ = 10 versus H_{a} : μ > 10$

Page 491
Invalid. Statistics such as $\bar{x}$ never appear in the hypotheses (though they are used later on in the hypothesis test procedure) because we know their values. Hypotheses are about parameters such as $μ$ , whose value is unknown. The correct form is:

$H_{0} : μ = 25 versus H_{a} : μ < 25$
Invalid. The same value for $μ_{0}$ should go in both $H_{0}$ and $H_{a}$ . One possible correct form is:

$H_{0} : μ = 98.6 versus H_{a} : μ > 98.6$
This form for the hypotheses is valid.

NOW YOU CAN DO

Exercises 9–12.