Research Methodology - Dr. Krishan K. Pandey

Sampling Fundamentals 181
(i) Find the expected value of the sample information (EVSI) * for every possible n;
(ii) Also workout reasonably approximated cost of taking a sample of every possible n;
(iii) Compare the EVSI and the cost of the sample for every possible n. In other words,
workout the expected net gain (ENG) for every possible n as stated below:
For a given sample size (n):
(EVSI) – (Cost of sample) = (ENG)
(iv) Form (iii) above the optimal sample size, that value of n which maximises the difference
between the EVSI and the cost of the sample, can be determined.
The computation of EVSI for every possible n and then comparing the same with the respective
cost is often a very cumbersome task and is generally feasible with mechanised or computer help.
Hence, this approach although being theoretically optimal is rarely used in practice.
Questions
1. Explain the meaning and significance of the concept of “Standard Error’ in sampling analysis.
2. Describe briefly the commonly used sampling distributions.
3. State the reasons why sampling is used in the context of research studies.
4. Explain the meaning of the following sampling fundamentals:
(a) Sampling frame;
(b) Sampling error;
(c) Central limit theorem;
(d) Student’s t distribution;
(e) Finite population multiplier.
5. Distinguish between the following:
(a) Statistic and parameter;
(b) Confidence level and significance level;
(c) Random sampling and non-random sampling;
(d) Sampling of attributes and sampling of variables;
(e) Point estimate and interval estimation.
6. Write a brief essay on statistical estimation.
7. 500 articles were selected at random out of a batch containing 10000 articles and 30 were found defective.
How many defective articles would you reasonably expect to find in the whole batch?
8. In a sample of 400 people, 172 were males. Estimate the population proportion at 95% confidence level.
9. A smaple of 16 measurements of the diameter of a sphere gave a mean X = 458 . inches and a standard
deviation σ s = 008 . inches. Find (a) 95%, and (b) 99% confidence limits for the actual diameter.
10. A random sample of 500 pineapples was taken from a large consignment and 65 were found to be bad.
Show that the standard error of the population of bad ones in a sample of this size is 0.015 and also show
that the percentage of bad pineapples in the consignment almost certainly lies between 8.5 and 17.5.
* EVSI happens to be the difference between the expected value with sampling and the expected value without sampling.
For finding EVSI we have to use Bayesian statistics for which one should have a thorough knowledge of Bayesian
probability analysis which can be looked into any standard text book on statistics.