Research Methodology - Dr. Krishan K. Pandey

Testing of Hypotheses I 203
to have been taken from a population with mean height 67.39" and standard deviation 1.30" at 5%
level of significance.
Illustration 3
Suppose we are interested in a population of 20 industrial units of the same size, all of which are
experiencing excessive labour turnover problems. The past records show that the mean of the
distribution of annual turnover is 320 employees, with a standard deviation of 75 employees. A
sample of 5 of these industrial units is taken at random which gives a mean of annual turnover as 300
employees. Is the sample mean consistent with the population mean? Test at 5% level.
Solution: Taking the null hypothesis that the population mean is 320 employees, we can write:
H0 : μ H = 320 employees
0
Ha: μ H ≠ 320 employees
0
and the given information as under:
X = 300 employees, σ p = 75 employees
n = 5; N = 20
Assuming the population to be normal, we can work out the test statistic z as under:
z
*
=
=
σ
p
X
− μ
/ n × N − n / N − 1
H
0
b gb g
300 − 320
20
=−
75/ 5 × 20 − 5 / 20 − 1 3354 . . 888
b g b g b gb g
= – 0.67
As H a is two-sided in the given question, we shall apply a two-tailed test for determining the
rejection regions at 5% level of significance which comes to as under, using normal curve area table:
R : | z | > 1.96
The observed value of z is –0.67 which is in the acceptance region since R : | z | > 1.96 and thus,
H 0 is accepted and we may conclude that the sample mean is consistent with population mean i.e.,
the population mean 320 is supported by sample results.
Illustration 4
The mean of a certain production process is known to be 50 with a standard deviation of 2.5. The
production manager may welcome any change is mean value towards higher side but would like to
safeguard against decreasing values of mean. He takes a sample of 12 items that gives a mean value
of 48.5. What inference should the manager take for the production process on the basis of sample
results? Use 5 per cent level of significance for the purpose.
Solution: Taking the mean value of the population to be 50, we may write:
: μ = 50
* Being a case of finite population.
H H
0 0