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 several Ethiopian spices; shiro wet', a legume-based mixture of chickpea flour and Ethiopian spiced pepper; and ye-atkilt 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
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

(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.

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(b) Plot the means. Give a short summary of how the iron content of foods depends upon the cooking pot.

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(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 interactions.

Answer 1

Answer: ---- Date: ----15/7/2019

A) The summary statistics is as follows:- StdDev N Мean Type of Pot Type of food 2,33 Legumes 4 0.11 Aluminium Meat 4 2.06 0.25 Vegetables 4. 1.23 0.23 Legumes 4 2,47 0.07 Clay Meat 4. 2.18 0.62 Vegetables 4 1.46 0.46 Legumes 4 3.67 0.17 Iron Meat 4.68 4. 0.63 Vegetables 4 2,79 0.24 Type of Pot StdDev Mean Aluminium 12 1.87 0.52 Clay 12 2.04 0.60 Iron 12 3.71 0.88 It is reasonable to pool the variance in the table 1above but not in the table 2

B) Plotting the means as follows:- 5 Bar Chart for Compairing 4 2 1 0 Vegetables Vegetables Legumes Vegetables Legumes Legumes Meat Meat Meat Aluminium Aluminium Aluminium Clay Clay Clay Iron Iron Iron Bar Chart for Compairing Means 5 4 3 2 Clay Aluminium Clay Aluminium Aluminium Clay Iron Iron Iron Vegetables Vegetables Vegetables Meat Legumes Legumes Legumes Meat Meat From the graphs, we can say pot made of iron has high iron content. LO

C) Using Excel we got the following results:- ANOVA Source of Variation Sample F crit df 2 12.44698 92.263128.53E-13 3.354131 2 4.648436 34.45649 4 0.660107 4.8930370.0042472727765 P-value SS MS 24.89396 3.7E-08 3.354131 Columns 9.296872 Interaction 2.640428 3.6425 270.134907 40.47376 35 Within Total As the p-value<0.05 for main factors as well as for interaction. Hence, we conclude that the main effect and interaction effect is significant.