Elementary Statistics and Computer Application

Examples

Exapmle 2

• The severity of a disease and blood group were studied in a research projest. The findings sre given in the following table, knowmn as the m xn contingency table. Can this severity of the condition and blood group are associated.
Severity of a disease classified by blood group in 1500 patients

Condition	Blood Groups				Total
	O	A	B	AB
Severe	51	40	10	9	110
Moderate	105	103	25	17	250
Mild	384	527	125	104	1140
Total	540	670	160	130	1500

Solution

• H0: The severity of the disease is not associated with blood group.
• H1: The severity of the disease is associated with blood group.
Calculation of Expected frequencies
 
Condition	Blood Groups				Total
	O	A	B	AB
Severe	39.6	49.1	11.7	9.5	110
Moderate	90.0	111.7	26.7	21.7	250
Mild	410.4	509.2	121.6	98.8	1140
Total	540	670	160	130	1500

Test statistic



• The d.f. associated with the is (3-1)(4-1) = 6

Calculations

Oi	Ei	Oi­-Ei	(Oi­-Ei)2	(Oi­-Ei)2/Ei
51	39.6	11.4	129.96	3.2818
40	49.1	-9.1	82.81	1.6866
10	11.7	-1.7	2.89	0.2470
9	9.5	-0.5	0.25	0.0263
105	90.0	15	225.00	2.5000
103	111.7	-8.7	75.69	0.6776
25	26.7	-1.7	2.89	0.1082
17	21.7	-4.7	22.09	1.0180
384	410.4	-26.4	696.96	1.6982
527	509.2	17.8	316.84	0.6222
125	121.6	3.4	11.56	0.0951
104	98.8	5.2	27.04	0.2737
Total				12.2347
• =12.2347
• Table value of for 6 d.f. at 5% level of significance is 12.59

Inference

• < tab
• We accept the null hypothesis.
• The severity of the disease has no association with blood group

Example 3

• In order to determine the possible effect of a chemical treatment on the rate of germination of cotton seeds a pot culture experiment was conducted. The results are given below
Chemical treatment and germination of cotton seeds

	Germinated	Not germinated	Total
Chemically Treated	118	22	140
Untreated	120	40	160
Total	238	62	300


• Does the chemical treatrment improve the germination rate of cotton seeds?
Solution:

• H0:The chemical treatment does not improve the germination rate of cotton seeds.
• H1: The chemical treatment improves the germination rate of cotton seeds.
• Level of significance = 1%

Test statistic






Table value

• (1) d.f. at 1 % L.O.S = 6.635

Inference

• < tab
• We accept the null hypothesis.
• The chemical treatmentwill not improve the germination rate of cotton seeds significantly.
Example 4

• In an experiment on the effect of a growth regulator on fruit setting in muskmelon the following results were obtained. Test whether the fruit setting in muskmelon and the application of growth regulator are independent at 1% level.
	Fruit set	Fruit not set	Total
Treated	16	9	25
Control	4	21	25
Total	20	30	50
Solution

• H0:Fruit setting in muskmelon does not depend on the application of growth regulator.
• H1: Fruit setting in muskmelon depend on the application of growth regulator.
• Level of significance = 1%
After Yates correction we have
 
	Fruit set	Fruit not set	Total
Treated	15.5	9.5	25
Control	4.5	20.5	25
Total	20	30	50

Tet statistic



Table value
(1) d.f. at 1 % level of significance is 6.635

Inference

• > tab
• We reject the null hypothesis.
• Fruit setting in muskmelon is influenced by the growth regulator. Application of growth regulator will increase fruit setting in musk melon.