Page 376 - DMTH404_STATISTICS

Statistics

Notes 2
æ N ö
N ad bc - ÷
-
ç
2
The value of c can now be obtained as  = è 2 ø .
2
(a b a c+ )( + )(b d+ )(c + ) d
Brand and Snedecor formula for a 2 ´ r Contingency table
For a 2 ´×r contingency table,

A 
A 1 A 2  A r Total
B 
2
B 1 a 1 a 2  a r a , the value of c can be directly computed by the use of the following
B b b  b b
2 1 2 r
Total n 1 n 2  n r N
formula :

2
2
N æ r a 2 a ö
2
 = çå i - ÷ with (r - 1) d.f.
ab è i= 1 n i N ø
Example 46: In a recent diet survey, the following results were obtained in an Indian
city:

No .of families Hindus Muslims Total
Tea takers 1236 164 1400
Non -tea takers 564 36 600
Total 1800 200 2000

Discuss whether there is any significant difference between the two communities in the matter
of taking tea? Use 5% level of significance.

Solution.
The null hypothesis to be tested can be written as H : There is no difference between the two
0
communities in the matter of taking tea.
2000 (1236 36 164 564´ - ´ ) 2
2
Using the direct formula, we have  = = 15.24.
1400 1800 200 600
´
´
´
2
The value of c from table for 1 d.f. and 5% level of significance is 3.84. Since the calculated value
is greater than the tabulated value, H is rejected.
0
Example 47: A certain drug is claimed to be effective in curing cold. In an experiment on
160 persons with cold, half of them were given the drug and the remaining half were given
sugar pills. The patients' reactions to the treatment are recorded in the following table :
Helped Harmed No effect Total
Drug 52 10 18 80
Sugar pills 44 10 26 80
Total 96 20 44 160

Test the hypothesis that the drug is no better than the sugar pills for curing cold.

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