Unit 2: statistical estimation

2.9 Sample Size determination in estimating proportion

The procedure just used is applicable to determining the sample size when proportions are involved. Three things must be specified:

1) You, the researcher, must decide on the level of confidence- usually .95 or .99
2) You must indicate how precise the estimate of the population proportion must be
3) the population proportion p, must be either approximated from past experience or approximated from a small pilot survey of, say, 50 or 100.

From the confidence interval estimation of population proportion

, The maximum allowable error E = . Solving for n, we get
n = pq .

n = p(1-p)

Sample size determination for proportion

where p – is the estimated proportion based on the past experience or a pilot survey.

Z_/2 – is the Z value associated with the degree of confidence selected.
E – is the maximum allowable error the researcher will tolerate.


2.11 Summary

The process of going from the known sample to the unknown population has been called statistical inference. The basic problem of sampling theory usually presents itself in one of two forms: (a) some feature of the population in which an enquirer is interested may be completely unknown to him, and he may want to make a guess about this feature completely on the basis of a random sample form the population. (b) Some information as to the feature of the population may be available to the enquirer, and he may want to see whether the information is tenable in the light of the random sample taken from the population. The first type of problem is the problem of estimation which is discussed in this section so far and the second one is the problem of testing of hypotheses, which will be dealt with in the next unit.

2.12 Glossary


Bias – A possible consequence if certain members of the population are denied the chance to be selected for the sample. As a result, the sample may not be representative of the population.
Confidence co-efficient – The value 1 - 
Confidence interval – The interval in which the parameter lies
Estimator – A function of the random samples used to estimate the parameter
Proportion – A fraction or percentage of a sample or a population having a particular trait.
Estimate – The numerical value of the statistic.