EXAMPLE 26 test for using the critical-value method
As a check on your arithmetic, the two quantities you obtain when checking the normality conditions should add up to . Here, .
Refer to Example 25. Test whether the population proportion of Chromebook computers has changed from 20%, using the critical-value method and level of significance .
Solution
First, we check that both of our normality conditions are met. From Example 25, we have and .
The normality conditions are met and we may proceed with the hypothesis test.
Step 1 State the hypotheses.
From Example 25, our hypotheses are
where represents the population proportion of computers that are Chromebooks.
Step 2 Find and state the rejection rule.
We have a two-tailed test, with . This gives us our critical value . the rejection rule from Table 11 is: Reject if or (Figure 35).
Figure 9.45: FIGURE 35 does not fall in the critical region.Step 3 Calculate .
From Example 25, we have
546
Step 4 State the conclusion and the interpretation.
The test statistic is not and not . Thus, we do not reject . There is insufficient evidence at level of significance that the population proportion of computers that are Chromebooks differs from 20%.
NOW YOU CAN DO
Exercises 15–18.