Small Scale Survey
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Example Sample Mean Distribution
According to the Central Limit Theorem, the sample mean is distributed Normally. The mean of the sample mean (the centre of the curve) is equal to the population mean. The shaded area in the diagram shows the population mean ± 1 standard error. According to the tables for the normal function, this comprises of 68% of the curve. This means that there is a 68% chance that the mean of the sample is within one standard error of the mean of the population. This probability can be written algebraically as an inequality:
However, as m is not known when sampling, the above inequality is useless, as it is not known to which number to add or subtract the standard error from. So the inequality is rearranged thus:
This shows that the probability that the population mean is within 1 standard error of the sample mean is 68%. In other words you can be 68% confident that the population mean is within 1 s.e. of the sample mean.
This idea can be used to calculate the confidence intervals that allow you to be 90%, 95% and 99% sure of the range where the population mean is found. Conf ...
