A medical researcher wishes to test the effects of 2 diets and the time of day on the sodium level in person’s blood. Eight people are randomly selected, and two are randomly assigned to each of the four groups. Analyze the data shown in the tables here, using a two-way ANOVA at a=0.05. The sodium content is measured in milliequivalents per liter.

**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 problem #11.**

**Source SS df. MS F**

Time 1800.0 1 1800 1800/69.75 = 25.81

Diet 242.0 1 242 242 / 69.75 = 3.47

Interaction 264.5 1 264.5 264.5 / 69.75 = 3.79

Within 279.0 4 279 / 4 = 69.75

Total 2585.5 7

The critical value for (1, 4) degrees of freedom and a 0.05 significance level is 7.7086. *From this we conclude that there's no interaction effect, the diet has no significant effect on the means, but Time has a significant effect on the means.*

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