Research Methodology - Dr. Krishan K. Pandey

180 Research Methodology
=
2 b2. 005g b. 02gb1−. 02gb4000g 2 2
b. 02g b4000 − 1g + b2. 005g b. 02gb1− . 02g
3151699 . 3151699 .
=
= = 187. 78 ~ 188
15996 . + . 0788 16784 .
But if the population happens to be infinite, then our sample size will be as under:
2
z ⋅ p ⋅q
n =
2
e
=
2 b2. 005g ⋅b. 02gb1− . 02g
2
. 02
b g
. 0788
= = 196. 98 ~ 197
. 0004
Illustration 7
Suppose a certain hotel management is interested in determining the percentage of the hotel’s guests
who stay for more than 3 days. The reservation manager wants to be 95 per cent confident that the
percentage has been estimated to be within ± 3% of the true value. What is the most conservative
sample size needed for this problem?
Solution: We have been given the following:
Population is infinite;
e = .03 (since the estimate should be within 3% of the true value);
z = 1.96 (as per table of area under normal curve for the given confidence level of 95%).
As we want the most conservative sample size we shall take the value of p = .5 and q = .5. Using
all this information, we can determine the sample size for the given problem as under:
2
z p q
n =
2
e
=
2 b196 . g ⋅b. 5gb1− . 5g
. 9604
= = 1067. 11 ~ 1067
2
. 03 . 0009
b g
Thus, the most conservative sample size needed for the problem is = 1067.
DETERMINATION OF SAMPLE SIZE THROUGH
THE APPROACH BASED ON BAYESIAN STATISTICS
This approach of determining ‘n’utilises Bayesian statistics and as such is known as Bayesian approach.
The procedure for finding the optimal value of ‘n’ or the size of sample under this approach is as under: