Question

what calculations can i use for a simple random sampling using a small sample size?

"What kind of calculations is asked should be mentioned properly the procedure the variance etc.

Answer 1

First off, to choose the right sample size for a simple random sample, you need to define the following inputs:

• Specify the desired margin of error ME. This is your measure of precision.

• Specify alpha.
  • For a hypothesis test, alpha is the significance level.
  • For an estimation problem, alpha is: 1 - Confidence level.

• Find the critical standard score z.
  • For an estimation problem or for a two-tailed hypothesis test, the critical standard score (z) is the value for which the cumulative probability is 1 - alpha/2.
  • For a one-tailed hypothesis test, the critical standard score (z) is the value for which the cumulative probability is 1 - alpha.

• Unless the population size is very large relative to sample size (e.g., 20 times larger), you need to specify the size of the population (N).

You will also need to know the variance of the population, s2. Given these inputs, the following formulas find the smallest sample size that provides the desired level of precision:

Sample Statistic	Population size	Sample Size
Mean	Known	n = { z2 * s2 * [ N / (N - 1) ] } / { ME2 + [ z2 * s2 / (N - 1) ] }
Mean	Unknown	n = ( z2 * s2 ) / ME2
Proportion	Known	n = [ ( z2 * p * q ) + ME2 ] / [ ME2 + z2 * p * q / N ]
Proportion	Unknown	n = [ ( z2 * p * q ) + ME2 ] / ( ME2 )

The following formulas can be used to determine the required statistics (mean, variance, standard deviation etc.):

Hope this helps!