1. CHAPTER 15 SUMMARY
Chapter Specifics
A parameter in a statistical problem is a number that describes a population, such as the population mean μ. To estimate an unknown parameter, use a statistic calculated from a sample, such as the sample mean .
The law of large numbers states that the actual observed mean outcome must approach the mean μ of the population as the number of observations increases.
The population distribution of a variable describes the values of the variable for all individuals in a population.
The sampling distribution of a statistic describes the values of the statistic in all possible samples of the same size from the same population.
When the sample is an SRS from the population, the mean of the sampling distribution of the sample mean is the same as the population mean μ. That is, is an unbiased estimator of μ.
The standard deviation of the sampling distribution of is σ/ for an SRS of size n if the population has standard deviation σ. That is, averages are less variable than individual observations.
When the sample is an SRS from a population that has a Normal distribution, the sample mean also has a Normal distribution.

2. Choose an SRS of size n from any population with mean μ and finite standard deviation σ. The central limit theorem states that when n is large, the sampling distribution of is approximately Normal. That is, averages are more Normal than individual observations. We can use the N(μ, σ/) distribution to calculate approximate probabilities for events involving .