Page 248 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 13: Test of Significance

5. The random variate t is defined as the ratio of a standard normal variate to the square root Notes
2
of  - variate divided by its degrees of freedom.

X    X    n
To show this we can write t  
s/ n s
Dividing numerator and denominator by , we get

 X    n  X     X   
t =    / n   / n
s s / 2 1  X  2
2
i
   X 
n 1  2

 X   

=  / n  Standard Normal Variate
 2 n 1  2 -variate

n  1

Illustration: There are two nourishment programmes ‘A’ and ‘B’. Two groups of children are
subjected to this. Their weight is measured after six months. The first group of children subjected
to the programme ‘A’ weighed 44,37,48,60,41 kgs. at the end of programme. The second group of
children were subjected to nourishment programme ‘B’ and their weight was 42, 42, 58, 64, 64, 67,
62 kgs. at the end of the programme. From the above, can we conclude that nourishment
programme ‘B’ increased the weight of the children significantly, given a 5% level of confidence.

Null Hypothesis: There is no significant difference between Nourishment programme ‘A’ and
‘B’.
Alternative Hypothesis: Nourishment programme B is better than ‘A’ or Nourishment
programme ‘B’ increase the children’s weight significantly.
Solution:

Nourishment programme Nourishment programme B
A
X x x x x  y y y y y 
2
2


= (x-46) =(y-57)
44 -2 4 42 -15 225
37 -9 81 42 -15 225
48 2 4 58 1 1 Contd...
60 14 196 64 7 49
41 -5 25 64 7 49
10
100
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