Sampling Distributions:
This section of your text book is mostly on the vocabulary listed below.
A population can be thought of as a set of measurements (or counts), either existing or
conceptual.
A sample is a subset of measurements from the population. The most important samples
are random samples.
A population parameter is a numerical descriptive measure of a population (usually a
random sample).
Examples: population mean (μ), population variance (σ2), population standard
deviation (σ), and the population proportion of successes (p) in a binomial distribution.
A statistic is a numerical descriptive measure of a sample (usually a random sample).
Examples: sample mean (x bar), sample variance (s2), sample standard deviation
(s), and the sample estimate (p hat = r/n) for the proportion of successes in a binomial
distribution.
*** Notice that for a given population a specified parameter is a fixed quantity, while the
statistic might vary depending on which sample has been selected.
Often we do not have access to all the measurements of an entire population, so we must
use measurements from a sample instead. In such cases, we will use statistic to make
inferences about corresponding population parameters. These principal types of
inference we will make are:
1) To estimate the value of a population parameter.
2) To formulate a decision about the value of a population parameter.
A sampling distribution is a type of probability distribution that is used to evaluate the
reliability of inference that we have made.
*** To see a sampling distribution view text p. 403 – 407.
Now, view guided exercise #1 on text p. 407 – 408.
Complete 7.1 problems on text p. 408.