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# Elem Stats ch 7

### A Brief Version: Elementary Statistics Ch 7

Point Estimate A specific value estimate of a parameter. The best point estimate of the population mean (mu) is the sample mean (X bar).
Estimators Sample measures are used to estimate population measures.
What are the properties of a good estimator? It should be an unbiased estimator. It should be a consistent estimator. It should be a relatively efficient estimator.
Estimation The process of estimating the value of a parameter from information obtained from a sample.
Unbiased Estimator The expected value or the mean of the estimates obtained from a given size is equal to the parameter being estimated.
Consistent estimator An estimator whose value approaches the value of the parameter estimated as the sample size increases.
Relatively Efficient Estimator An estimator that has the smallest variance from among all the statistics that can be used to estimate a parameter.
Interval Estimate (of a parameter) An interval of a range of values used to estimate the parameter. This estimate may or may not contain the value of the parameter being estimated.
Confidence Level (of an interval estimate of a parameter) The probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter repeated.
Confidence Interval A specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate.
Maximum Error of the Estimate (E) The maximum likely difference between the point estimate of a parameter and the actual value of the parameter.
The t distribution is similar to the standard normal distribution in these ways: It is bell shaped. It is symmetric about the mean. The mean, median, and mode are equal to 0 and are located at the center of the distribution. The curve never touches the x axis.
The t distribution differs from the standard normal distribution in these ways: The variance is greater than 1. A family of curves based on the concept of degrees of freedom, which is related to sample size. As the sample size increases the t distribution approaches the standard normal distribution.
Degrees of Freedom (df) The number of values that are free to vary after a sample statistic has been computed, and they tell the researcher which specific curve to use when a distribution consists of a family of curves. (n - 1)
Proportion A part of a whole, represented by a fraction, decimal, or a percentage.
Chi-Square Distribution ("ki") A probability distribution obtained from the values of (n-1)*s squared/ sigma squared when random samples are selected from a normally distributed population whose variance is sigma squared.
Created by: dengler