GGR 270 – Lecture 7 – October 27, 2010

Central Limit Theorem II

The frequency of sample means will be normally distributed

When the sample size is large, the sample mean is likely to be quite close to the

population mean

A large sample is more likely to be closer to the true population mean than a smaller

sample

Variability

Standard deviation of the sampling distribution is equal to the sample standard

deviation divided by the square root of the sample size

This is called the standard error of the mean

oIndicates how much a typical sample mean is likely to differ from the true

population mean

oMeasures the amount of sampling error

oThe larger the sample size (n), the smaller the amount of sampling error

How large is large

If sampled population is normal, then sampling distribution of means will also be

normal, no matter what the sample size

If the sampled population is approximately normal, then the sampling distribution of

means will be approximately normal for relatively small sample sizes

When the population is skewed, the sample size must be large (n>30) before the

sampling distribution will become normal

Sample Estimation

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