Research Methodology - Dr. Krishan K. Pandey

224 Research Methodology
Solution: Let H0 : p$ = p (there is no difference between sample proportion and population proportion)
and Ha : p$ ≠ p (there is difference between the two proportions)
and on the basis of the given information, the test statistic z can be worked out as under:
z =
p$ − p
N − n
p ⋅ q
nN
=
20
− . 05
100
2000 − 100 b. 05gb. 95gb100gb2000g 0150 .
= = 7143 .
0. 021
As the H is two-sided, we shall determine the rejection regions applying two-tailed test at 5 per
a
cent level and the same works out to as under, using normal curve area table:
R : | z | > 1.96
The observed value of z is 7.143 which is in the rejection region and as such we reject H and 0
conclude that there is a significant difference between the proportion of smokers in the college and
university.
HYPOTHESIS TESTING FOR COMPARING A VARIANCE
TO SOME HYPOTHESISED POPULATION VARIANCE
The test we use for comparing a sample variance to some theoretical or hypothesised variance of
population is different than z-test or the t-test. The test we use for this purpose is known as chisquare
test and the test statistic symbolised as χ 2 , known as the chi-square value, is worked out.
2 2
The chi-square value to test the null hypothesis viz, H0: σs = σp
worked out as under:
where σ s 2 = variance of the sample
2
σ p = variance of the population
χ
2
2
σs
= n − 1
2
σ
p
b g
(n – 1) = degree of freedom, n being the number of items in the sample.
Then by comparing the calculated value of χ 2 with its table value for (n – 1) degrees of
freedom at a given level of significance, we may either accept H 0 or reject it. If the calculated value
of χ 2 is equal to or less than the table value, the null hypothesis is accepted; otherwise the null
hypothesis is rejected. This test is based on chi-square distribution which is not symmetrical and all