Question

Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have been largely replaced by aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked in iron pots will contain more iron than food cooked in other types of pots. One study designed to investigate this issue compared the iron content of some Ethiopian foods cooked in aluminum, clay, and iron pots. Foods considered were yesiga wet beef cut into small pieces and prepared with severa Ethiopian s cesi shro et a legume-based mixture of chick ea flour and Etiopian spiced pepper and re-at . allych'a, a lightly spiced vegetable casserole. Four samples of each food were cooked in each type of pot. The iron in the food is measured in milligrams of iron per 100 grams of cooked food. The data are shown in the table below Iron Content (mg/100 g) of Food Cooked in Different Pots Legumes Type of potMeat Aluminum 177 2.36 1.96 2.14 2.40 2.17 2.412.34 1.03 1.53 1.071.30 Clay Iron Vegetables 2.2기1.28 2.48 2.682.412.432.572·48|||1.55|0.791 1.68|1.82 5.27 5.17 4.06 4.22 3.69 3.43 3.84 3.72 2.45 2.99 2.80 2.92 (a) Make a table giving the sample size, mean, and standard deviation for each type of pot. Is it reasonable to pool the variances? Although the standard deviations vary more than we would like, this is partially due to the small sample sizes, and we will proceed with the analysis of variance. This answer has not been graded yet. (b) Plot the means. Give a short summary of how the iron content of foods depends upon the cooking pot. This answer has not been graded yet. (c) Run the analysis of variance. Give the ANOVA table, the F statistics with degrees of freedom and P-values, and your conclusions regarding the hypotheses about main effects and nteractions.

Answer 1

Type of Pot	sample size	mean	standard deviation
Aluminum	12	1.8733	0.5223
Clay	12	2.0367	0.6013
Iron	12	3.7133	0.8843

Comment: The maximum standard deviation is less than twice the minimum standard deviation. Hence, it is reasonable to pool the variance. Here, standard deviations do not vary more than we would like and will proceed with the analysis of variance.

b)

Mean of iron content 4.0000 3.5000 3.0000 2.5000 2.0000 1.5000 1.0000 0.5000 0.0000 Aluminum Clay Iron

From the above graph, the iron content to the aluminum and clay pots are approximately equal. But, it is different from an iron pot.

c)

Two-way ANOVA: Iron versus Type of Pot, Food coke

Source	DF	SS	MS	F	P
Type of Pot	2	24.8940	12.4470	92.26	0.000
Food coke	2	9.2969	4.6484	34.46	0.000
Interaction	4	2.6404	0.6601	4.89	0.004
Error	27	3.6425	0.1349
Total	35	40.4738

S = 0.3673 R-Sq = 91.00% R-Sq(adj) = 88.33%

Comment: The estimated p-value for interaction is 0.004. Hence, there is an effect of the interaction of the Type of pots and Food cook at the 0.05 significance level. Now, the effect of the main does not give meaningful reason due to significant interaction.