Page 84 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes Self Assessment

Fill in the blanks:
17. Greater the desired precision, __________will be the sample size
18. There is a trade off between the degree of confidence and the degree of ____________with
a sample of fixed size.

4.7 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, s /n) since the underlying population is normal.
2
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:

 
z
n
where  is the standard deviation of the population distribution of that quantity and n is the size
(number of items) in the sample.

Self Assessment

Fill in the blanks:
19. Sampling distribution depends on the underlying distribution of the ...............................,
the statistic being considered, and the sample size used.
20. The standard deviation of the sampling distribution of the statistic is referred to as the
............................... of that quantity

4.8 Summary

 Sample is a representative of population while Census represents cent percent of
population.

 The most important factors distinguishing whether to choose sample or census is cost and
time. There are seven steps involved in selecting the sample.
 There are two types of sample, namely, Probability sampling and Non-probability sample.

 Probability sampling includes random sampling, stratified random sampling systematic
sampling, cluster sampling, Multistage sampling.

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