EXAMPLE 1 Verify the requirements for performing an analysis of variance

dormitory

Verify the requirements for performing an analysis of variance using the hypotheses

where represents the population mean GPA for Dormitory , using data from Table 1.

Solution

  • Step 1 Normality. To verify that each of the populations is normally distributed, we examine normal probability plots of each sample, shown in Figure 5. Each plot indicates acceptable normality.

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    Figure 12.5: FIGURE 5 Normal probability plots verify normality requirement.

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  • Step 2 Equal Variances. To find the standard deviation for Dorm A, we first find

    Then

    We similarly find and . The largest, , is not larger than twice the smallest, . Thus, the equal variance require-ment is satisfied.

  • Step 3 Independence. Because the students are randomly sampled from each dormitory, with the selection of students in one dormitory not affecting the selection of students sampled from the other dormitories, the independence assumption is also validated.

Note: We retain many decimal places when calculating , , and because these values are used to calculate other quantities later on.

NOW YOU CAN DO

Exercises 7–10.