Chapter 6 Terms

Sampling Distrubution

the probability of a sample statistic

Minimum Variance

among estimators, the estimator with the minimum variance is the estimator that has the smallest standard error for its sampling distribution.

Variance

Population Parameter: δ² Sample Statistic: s²

Mean

Population Parameter: μ Sample Statistic: x̄

Properties of the Sampling Distribution of x̄

* The mean of the sampling distribution of x̄ equals the mean of the sampled population. That is, μx̄ = E(x̄) = μ *The standard deviation of the sampling distribution of x̄ equals standard deviation of sampled population ------------------------------------------------------- square root of sample size That is, δx̄ = δ/√n

Parameter

A numerical descriptive measure of a population. Because it is based on the observations in the population, the value is almost always unknown.

Sample Statistic

A numerical descriptive measure of a sample. It is calculated from the observations in the sample

Minimum Variance Unbiased Estimator (MVUE)

An estimator that is unbiased and has the smallest variance among all unbiased estimators. If μx̄ = μ, then statistic x̄ is an unbiased estimator of μ.

Theorem 6.2: Central Limit Theorem

Consider a random sample of n observations selected from a population (ANY population) with mean μ and standard deviation δ. Then, when n is sufficiently large, the sampling distribution of x̄ will be approximately a normal distribution with mean μx̄ = μ and a standard deviation δx̄=δ/√n. The larger the sample size, the better will be the normal approximation to the sampling distribution of x̄

Theorem 6.1

If a random sample of n observations is selected from a population with a normal distribution, the sampling distribution of x̄ will be a normal distribution

Biased Estimate

If the mean of the sampling distribution is not equal to the parameter, the statistic is said to be a ______ ________ of the parameter

Unbiased Estimate

If the sampling distribution of a sample statistic has a mean equal to the population parameter the statistic is intended to estimate, the statistic is said to be an ________ ________

Binomial Proportion

Population Parameter: p Sample Statistic: p̂

Standard Deviation

Population Parameter: δ Sample Statistic: s

The Probability Distribution of the Statistic

The sampling distribution of a sample statistic calculated from a sample of n measurements; it is the probability distribution for all of the possible values of the statistic that could result when taking samples of size n.

Standard Error of the Mean

The standard deviation δx̄

Point Estimator

a rule or formula that tells us how to use the sample data to calculate a single number that can be used as an estimate of the population parameter

A

if two alternative sample statistics are both unbiased, the one with the smaller standard deviation is preferred; _ is preferred