Research Methodology - Dr. Krishan K. Pandey

170 Research Methodology
n = 36
X = 40 years
σ s = 45 . years
and the standard variate, z, for 95 per cent confidence is 1.96 (as per the normal curve area table).
Thus, 95 per cent confidence inteval for the mean age of population is:
s X ± z
n
σ
or 40 196 45 .
± .
36
b gb g
or 40 ± 196 . 0. 75
or 40 ± 147 . years
Illustration 2
In a random selection of 64 of the 2400 intersections in a small city, the mean number of scooter
accidents per year was 3.2 and the sample standard deviation was 0.8.
(1) Make an estimate of the standard deviation of the population from the sample standard
deviation.
(2) Work out the standard error of mean for this finite population.
(3) If the desired confidence level is .90, what will be the upper and lower limits of the confidence
interval for the mean number of accidents per intersection per year?
Solution: The given information can be written as under:
N = 2400 (This means that population is finite)
n = 64
X = 32 .
σs = 08 .
and the standard variate (z) for 90 per cent confidence is 1.645 (as per the normal curve area table).
Now we can answer the given questions thus:
(1) The best point estimate of the standard deviation of the population is the standard deviation
of the sample itself.
Hence,
σ$ = σ = 08 .
p s
(2) Standard error of mean for the given finite population is as follows:
σ
X
σ s
= ×
n
N − n
N − 1