To know population mean reflect on the sample mean, we need to know the sample distribution of the sample mean.

Sampling distribution：all possible values that can be assumed by that statistic, computed from samples of the same size drawn from the same population

In any particular sample the sample mean (or sample variance) will (almost certainly) not equal to population meanμ

(or variance 2)

Sampling error: The difference between a sample statistic & the population parameter

This error is not a mistake it is a cost of sampling

This cost can be reduced by taking larger samples

Other errors such as mistakes in collecting raw data are likely to occur but are ignored at present

Standard deviation of the sampling distribution is called the standard error (se)

Sample mean has a sampling distribution also has a (population) mean

Mean of the sampling distribution of the sample mean is equal to the population mean

Population distribution of X is normal

Sample mean is also normal Eg: From past experience X is well approximated by a normal distribution with m = $40 & s = $10

If an auditor takes a random sample of 25 accounts what is the probability that the mean balance would be less than $36

Central Limit Theorem (CLT)

The sampling distribution of the mean of a random sample drawn from any population with mean & variance2 will be approximately normally distributed for a sufficiently large sample size

A sufficiently large sample implies it is not necessary to assume normality of the underlying population to make inferences about the sample mean based upon the normal distribution

When sample size is large, nothing has changed.…