Page 164 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 8: Sampling and Sampling Distribution

This implies that those who don’t respond should be motivated. It can be done in any one of the Notes
following ways:
1. An advance letter informing the respondents that they will receive a questionnaire and
requesting their cooperation. This will generally increase the rate of response.
2. Monetary incentive or gift given to respondents will yield a larger response rate.
3. Proper follow up is necessary after the potential respondent received the questionnaire.

Example: Determine the sample size if standard deviation of the population is 3.9,
population mean is 36 and sample mean is 33 and the desired degree of precision is 99%.
Solution: Given   3.9 ,   36,x  33 and z = 1% (99% precision implies 1% level of significance)

i.e. z = 2.576 (at 1% l.o.s) (Table value)
We know that sample size n can be obtained using the relation

2
 z  

n =   where d    x
 d 

 2.576 3.9 2
=    11.21  11
 36 33 


Task Prepare a sample plan including the sample size for Santoor soap, keeping in mind
both the male and female customers. Use three economic strata, the educational level and
the age group influencing the buyer behaviour. Prepare a sampling design for the
following:

1. To measure the effectiveness for a TV Ad on soaps.
2. Consumer reaction to a new brand of coffee introduced.
3. To assess the market share of branded soap.

8.7 Sampling Distribution

A sampling distribution is the probability distribution of a given statistic based on a random
sample of certain size n. It may be considered as the distribution of the statistic for all possible
samples of a given size. The sampling distribution depends on the underlying distribution of
the population, the statistic being considered, and the sample size used. The sampling distribution
is frequently opposed to the asymptotic distribution, which corresponds to the limit case .

Example: Consider a normal population with mean and variance. Assume we
repeatedly take samples of a given size from this population and calculate the arithmetic
mean for each sample – this statistic is called the sample mean. Each sample will have its
own average value, and the distribution of these averages will be called the “sampling
distribution of the sample mean”. This distribution will be normal N(m, s2/n) since the
underlying population is normal.
The standard deviation of the sampling distribution of the statistic is referred to as the standard
error of that quantity. For the case where the statistic is the sample mean, the standard error is:

LOVELY PROFESSIONAL UNIVERSITY 159