Defining the size of the random sample based upon expected means

Question: How large should my sample be if I want the actual mean of the population to be in a specific range around the measured mean of the sample?

Essential factors for this calculation are:

1. The expected extent of the standard deviation

i.e. the distribution of the mean values measured in the sample.
If the standard deviation is unknown, the rule of thumb is used:
(maximum of the scale – minimum of the scale)/3.

2. The maximum tolerated difference of means

i.e. the maximum extent the actual mean of the population may deviate from the mean of the sample.

3. The desired significance level

i.e. the statistical probability that the actual mean of the population is within the tolerated range of variation around the measured mean of the sample - in market research, we normally target a significance level of 95%.