2. 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
3. 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
4. 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
• 𝜎 𝑥 = = The standard deviation of the sample
𝑛
averages is equal to the population standard
deviation divided by the square root of the
sample size
5. Sampling Error
• Sampling error is the variability we expect to
see from one sample to another – also called
sampling variability
