Chapter 7 - Probability and Sample Means

Sample Mean Z-Score

• z-score to describe an entire sample

• follows the same standardized normal distribution

  • 0 = average/central/representative sample

  • ± 2.00 = extreme score

Distribution of Sample Means

• the collection of sample means from all possible random samples (of a particular size) that can be obtained from a population

  • distribution of scores instead of means

Central Limit Theorem

• often, we can’t actually know the value of the population mean and every possible sample mean derived from this population

• used to estimate if your distribution of sample means is normal

Your distribution of sample means will be normal if:

• the population from which the samples are selected is a normal distribution

  • used less often because we don’t usually know if a population is normally distributed

  • test sample from a population we already know is normal — sample is normal too

• the sample size (n) is at least 30

  • head rule — first rule doesn’t matter if this one is satisfied

Mean of the Distribution of Sample Means

• the average value of sample means will be equal to the population mean

• expected value of M = the mean of the distribution of sample means

  • expected value of M will always equal the population mean

Standard Error

• the average distance between a sample mean and the population mean

• sometimes called standard error of M

• a new spin on standard deviation (standard deviation of the distribution of sample means)

• tells you how well your sample represents the population

Sampling Error

• the natural discrepancy (or error) between a sample statistic and the population

Small Standard Deviation

• sample means are closer together

• sample mean is a more reliable estimate of the population

*aim for small

Large Standard Error

• sample means are more spread apart/different

• sample mean is a less reliable estimate of the population

Standard Error: Law of Large Numbers

• as sample size increases, standard error decreases

• a larger sample is better able to represent the population

• want a sample of at least 30 (bare minimum)