Iron-deficiency anemia is the most common form of malnutritionin developing countries, affecting about 50% of children and womenand 25% of men. Iron pots for cooking foods had traditionally beenused in many of these countries, but they have been largelyreplaced by aluminum pots, which are cheaper and lighter. Someresearch has suggested that food cooked in iron pots will containmore iron than food cooked in other types of pots. One studydesigned to investigate this issue compared the iron content ofsome Ethiopian foods cooked in aluminum, clay, and iron pots. Foodsconsidered were yesiga wet', beef cut into small piecesand prepared with several Ethiopian spices; shiro wet', alegume-based mixture of chickpea flour and Ethiopian spiced pepper;and ye-atkilt allych'a, a lightly spiced vegetablecasserole. Four samples of each food were cooked in each type ofpot. The iron in the food is measured in milligrams of iron per 100grams of cooked food. The data are shown in the table below.
| | Iron Content (mg/100 g) of Food Cooked inDifferent Pots |
|---|
| Type of pot | | Meat | | Legumes | | Vegetables |
|---|
| Aluminum | | 1.77 | 2.36 | 1.96 | 2.14 | | 2.40 | 2.17 | 2.41 | 2.34 | | 1.03 | 1.53 | 1.07 | 1.30 |
|---|
| Clay | | 2.27 | 1.28 | 2.48 | 2.68 | | 2.41 | 2.43 | 2.57 | 2.48 | | 1.55 | 0.79 | 1.68 | 1.82 |
|---|
| Iron | | 5.27 | 5.17 | 4.06 | 4.22 | | 3.69 | 3.43 | 3.84 | 3.72 | | 2.45 | 2.99 | 2.80 | 2.92 |
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(a) Make a table giving the sample size, mean, and standarddeviation for each type of pot. Is it reasonable to pool thevariances? Although the standard deviations vary more than we wouldlike, this is partially due to the small sample sizes, and we willproceed with the analysis of variance.
(b) Plot the means. Give a short summary of how the iron content offoods depends upon the cooking pot.
(c) Run the analysis of variance. Give the ANOVA table, the Fstatistics with degrees of freedom and P-values, and yourconclusions regarding the hypotheses about main effects andinteractions.
