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 picces and prepared with several Ethiopian spices; shiro wet', a lcgume-based mixture of chickpea flour and Ethiopian spiced pepper; and ye-atkit alycha, a lighdy spiced vegetable casserole. Four samples of each food were cooked in each type of pot. The iron in the food is measured in miligrams 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 tables 1.03 2.40 2.17 2.41 2.34 241 2.43 2.57 2.48 2.69 3.43 3.84 3.72 1.77 2.36 1.96 2.14 2.27 2.48 2.68 5.27 5.17 4.06 4.22 1.07 1.30 1.55 0.79 1.68 1.82 2.45 2.99 2.90 2.92 iron (e) Identify the factors in this experiment O Type of pot and cooking time Type of food and type of pot O Type of pot and iron content of food o Type of food and iron content of food (b) Assume standard deviations are approximately equal and analyze the data using two-way ANOVA with replication. Use Excel and enter the data as you see it in the table above. What is the F-value for the sample? (type of pot)? Round your answer to 2 decimal places. What is the F-value for the columns (type of food)? Round your answer to 2 decimal places. What is the F-value for the interaction? Round your answer to 2 decimal places. (c) Which factors have statistically significant p-values? Choose all that apply D Food type O Pot type No factors are statistically significant

Answer 1

data

	Meat	Legumes	Vegatable
Aluminium	1.77	2.4	1.03
	2.36	2.17	1.53
	1.96	2.41	1.07
	2.14	2.34	1.3
Clay	2.27	2.41	1.55
	1.28	2.43	0.79
	2.48	2.57	1.68
	2.68	2.48	1.82
	5.27	3.69	2.45
	5.17	3.43	2.99
Iron	4.06	3.84	2.8
	4.22	3.72	2.92

Data -> data analysi -> Anova: Two-factoe with replication

result

Anova: Two-Factor With Replication
SUMMARY	Meat	Legumes	Vegatable	Total
Aluminium
Count	4	4	4	12
Sum	8.23	9.32	4.93	22.48
Average	2.0575	2.33	1.2325	1.873333
Variance	0.063491667	0.012333	0.053492	0.27277
Clay
Count	4	4	4	12
Sum	8.71	9.89	5.84	24.44
Average	2.1775	2.4725	1.46	2.036667
Variance	0.386025	0.005092	0.211667	0.361606
Count	4	4	4	12
Sum	18.72	14.68	11.16	44.56
Average	4.68	3.67	2.79	3.713333
Variance	0.394733333	0.0298	0.057533	0.78197
Total
Count	12	12	12
Sum	35.66	33.89	21.93
Average	2.971666667	2.824167	1.8275
Variance	1.824724242	0.406808	0.60273
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Pot type	24.89395556	2	12.44698	92.26312	8.53E-13	3.354131
Food type	9.296872222	2	4.648436	34.45649	3.7E-08	3.354131
Interaction	2.640427778	4	0.660107	4.893037	0.004247	2.727765
Within	3.6425	27	0.134907
Total	40.47375556	35

a)

option B)

type of food and type of pot

b)

F-value of Pot type = 92.26

F-valur for Food type =34.46

F-value for interaction = 4.89

c)

all three factors have significant p-values as p-values < 0.05 in each case

option A),B) and C) are correct