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

  1. Invalid. The equal sign always goes in . So the correct form is:

    491

  2. Invalid. Statistics such as 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 , whose value is unknown. The correct form is:

  3. Invalid. The same value for should go in both and . One possible correct form is:

  4. This form for the hypotheses is valid.

NOW YOU CAN DO

Exercises 9–12.