EXAMPLE 6 Performing one-way ANOVA using the critical-value method

micemaze

Use the data from Example 5 to test, using the critical-value method and level of significance , whether the population mean time spent in the open-ended sections of the maze was the same for all three groups.

Solution

The conditions for performing ANOVA were verified in Example 5.

  • Step 1 State the hypotheses.

    where the represent the population mean time spent in the open-ended sections of the maze for each group.

  • Step 2 Find the critical value and state the rejection rule. The one-way ANOVA test is a right-tailed test, so the -critical value is the value of the distribution for and that has area to the right of it (see Figure 16). Here, and . To find , we may use the F tables or technology. To find our using Excel, enter = FINV(0.01,2,42) in cell A1, as shown in Figure 15. Thus, . ANOVA is a right-tailed test, so we will reject if .
    image
    Figure 12.15: FIGURE 15 Using Excel to find the critical value.
  • Step 3 Calculate . From Example 5, we have .
  • Step 4 State the conclusion and interpretation. Because (Figure 16), we reject . There is evidence that not all population mean times spent in the open-ended sections of the maze are equal.
    image
    Figure 12.16: FIGURE 16 has area of to the right of it.

NOW YOU CAN DO

Exercises 29–30.