Sampling Means

Bias of a Statistic

• Sampling may be bias is the sample proportions or sample means are skewed away from the known population mean or population proportion

• This bias is different from experimental bias –this is the result of poor sampling not a poorly conducted experiment or survey

Central Limit Theorem

• The mean of a random sample is a random variable whose sampling distribution can be approximated by the Normal distribution model. The larger the sample, the closer it is to the true Normal distribution and the better the approximation it is.

• Conditions:

• SRS, Independence, Large Enough Sample

Sampling Distribution for a Mean

• No matter what population the random sample comes from, the shape of the sampling distribution is approximately Normal

• 𝑥 = 𝑚𝑒𝑎𝑛 𝑜𝑓 1 𝑠𝑎𝑚𝑝𝑙𝑒 with sample size n• 𝜇 𝑥 = 𝜇 The mean of the sample means is equal

to the mean of the population

• 𝜎 𝑥 =𝜎

𝑛= The standard deviation of the sample

averages is equal to the population standard deviation divided by the square root of the sample size

Sampling Error

• Sampling error is the variability we expect to see from one sample to another – also called sampling variability