a number that describes the population. In statistical practice, the value of a parameter is not known because we cannot examine the entire population.
a number that can be computed from the sample data without making use of any unknown parameters. In practice, we often use a statistic to estimate an unknown parameter.
Remember s and p:
-statistics come from samples
-parameters come from populatoins.
Dinstinguishing between sample and population
-We write the Greek letter mu for the mean of a population and the Greek letter sigma for the standard deviation of a population. These are fixed parameters that are unknown when we use a sample for inference.
-The mean of the sample is the familiar xmean, the average of the observations in the population standard deviation sigma sample.
-The standard deviation of the sample is denoted by s, the standard deviation of the observations in the sample.
-• These are statistics that would almost certainly take different values if we chose another sample from the same population. The sample mean xmean sample standard deviation s from a sample or an experiment are estimates of the mean mu and standard deviation sigma of the underlying population.
- uses sample data to draw conclusions about the entire population. Because good samples are chosen randomly, statistics such as xmean computed from these samples are random variables. We can describe the behavior of a sample statistic by a probability model that answers the question: what would happen if we did this many times?
Law of Large Number
Draw observations at random from any population with a finite mean mu. As the number of observations drawn increases, the mean xmean of the observed values gets closer and closer to the mean mu of the population.