How to determine the Sample size in order to estimate population mean in a survey research study

How to determine the Sample size in order to estimate population mean in a survey research study

Researchers are normally confronted with the question, “How large a sample size do I need in the present research study?” The answer depends on a number of factors. The answer is different depending on whether the study is a survey designed to find out the mean of a parameter, or is designed to find its sample proportion. Thus, we consider here the case of estimating a mean.

Sample size to estimate a mean

Supposing one is interested to determine the mean number of marks obtained by Economics students of a University in a examination. Question asked is, “How large a sample size do I need?” To answer a question like this, the researcher need to decide how accurately (margin of error) does he need the answer and at what level of confidence does he intend to use the estimate. Also one need to know from some experience about what is the current estimate of the mean of Economics students of that University?

Calculation of sample size:

We are designing a survey or an experiment to estimate a population mean. In this case, the formula is ME = t s /√ n, where

• ü  ME is the desired margin of error
• ü  t is the t-score that we use to calculate the confidence interval, that depends on both the degrees of freedom and the desired confidence level,
• ü  s is the standard deviation,
• ü  n is the sample size we want to find.

A. We need a margin of error say, less than 1 mark.

B. 95% confidence intervals are typical but not in any way mandatory — we could do 90%, 99% or something else entirely. For this example, we assume 95%. Here, the sample size affects t as well as n. However, when n ≥ 30, the value of t is quite close to the value of z that we would get if we ignore the distinction between the normal and t distributions, so often we do ignore that distinction and just use the z value, e.g. 1.96 for a 95% confidence interval and so on.

C. In this case we need to specify s. In practice, s will be the sample standard deviation, computed after the sample is taken. So we can’t possibly know that in advance. But s is typically a guess, based either on past experience or on rough estimates of what sort of variability we would expect.

Taking an Example. We would like to estimate the mean Economics marks in the University under consideration, with 95% confidence, to accuracy within 0.5 marks. In such situations, we have literally no idea what s would be. So in the absence of anything better, let’s use that as our guess for s as say 2. In this case the 95% confidence interval translates to a z or t of 1.96. Therefore, equation becomes 0.5 = 1.96 × 2 /√ n which solves to n = (1.96 × 2 / 0.5)² = 61.47 or 61 to the nearest whole number.