Page 374 - DMTH404_STATISTICS

Statistics

Notes
Firm 
A B C
D
Type of labour 
Skilled 24 24 23 49

Semi -skilled 32 60 37 51

Manual 24 56 40 80

Solution.
H : There is no relation between the firm and the nature of labour.
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Calculation of Expected Frequencies

Firm 
A B C D Total
labour 
80 120 140 120 100 120 180 120
´
´
´
´
Skilled 500 500 500 500 120
= 19.2 = 33.6 = 24.0 = 43.2
80 180 140 180 100 180 180 180
´
´
´
´
Semi -skilled 500 500 500 500 180
= 28.8 = 50.4 = 36.0 = 64.8
80 200 140 200 100 200 180 200
´
´
´
´
Manual 500 500 500 500 200
= 32.0 = 56.0 = 40.0 = 72.0
Total 80 140 100 180 500
We note that the totals of corresponding rows or columns are same for the observed as well as
the expected frequencies.
2
2
From the observed and the expected frequencies, we get c = 12.81. Further, the value of c from
the table for (4 - 1)(3 - 1) = 6 d.f. and 5% level of significance is 12.59. Since the calculated value is
greater than the tabulated value H is rejected.
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Example 44: Samples of household income were taken from four cities. Test whether the
cities are homogeneous with regard to the distribution of income?
Cities 
A B C D Total
)
Income (Rs 
Under 3000 10 15 15 10 50
3000-5000 5 10 15 10 40
Over 5000 15 15 10 20 60
Total 30 40 40 40 150

Solution.
H : Various cities are homogeneous with regard to the distribution of income.
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