Page 251 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes 13.2 Large Sample Test

13.2.1 Z-test (Parametric Test)

(a) When sample size is > 30
P = Proportion in sample 1
1
P = Proportion in sample 2
2

Example: You are working as a purchase manager for a company. The following
information has been supplied by two scooter tyres manufacturers.
Company A Company B
Mean life (in km) 13000 12000
S.D (in km) 340 388
Sample size 100 100

In the above, the sample size is 100, hence a Z-test may be used.
(b) Testing the hypothesis about difference between two means: This can be used when two
population means are given and null hypothesis is Ho : P1 = P2.

Example: In a city during the year 2000, 20% of households indicated that they read
‘Femina’ magazine. Three years later, the publisher had reasons to believe that circulation has
gone up. A survey was conducted to confirm this. A sample of 1,000 respondents were contacted
and it was found 210 respondents confirmed that they subscribe to the periodical ‘Femina’. From
the above, can we conclude that there is a significant increase in the circulation of ‘Femina’?
Solution:
We will set up null hypothesis and alternate hypothesis as follows:
Null Hypothesis is H . µ = 15%
0
Alternate Hypothesis is HA. µ > 15%
This is a one-tailed (right) test.
P-
Z =
 1   
n
210
-0.20
1000
Z =
0.20 1 0.20 
1000
0.21-0.20
Z =
0.2 0.8

1000
0.01-
=
0.16
1000

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