Two programs in outdoor survival are available for army recruits. One lasts one week and the other lasts 2 weeks. The officer wishes to test the effectiveness of the programs and see whether there are any gender differences. Six subjects are randomly assigned to each of the programs according to gender. After completing the program, each is given a written test on his or her knowledge of survival skills. The test consists of 100 questions. The scores of the groups are shown here. Use a=0.10 and analyze the data, using a two-way ANOVA.

**Solution: **We need to test for

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and for

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and

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The ANOVA summary table is shown below:

**ANOVA summary table for #13.**

**Source SS d.f. MS F**

Gender 57.042 1 57.042 _{}

Duration 7.042 1 7.042 _{}

Interaction 3978.375 1 3978.375 _{}

Within 1365.500 20 _{}

Total 5407.959 23

The critical value for (1, 20) degrees of freedom and a 0.05 significance level is 4.3512. *From this we conclude that the only significant effect over means is the interaction between Duration and Gender, at the 0.05 significance level.*

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