Chapter 7 The Sampling Dist of the Sample Mean

Sampling error

error resulting from using a sample to estimate a population characteristic

Sampling Dist of the Sample Mean

For variable x, and a given sample size, the distribution of the mean is called the sampling dist of the sample mean

Mean of the Sample mean

For samples of size n, the mean of the variable mean equals the mean of the variable under consideration

Mean xbar= mean

Standard Deviation of the Sample Mean

For samples of size, the SD of the variable xbar equals the SD of the variable under consideration divided by the square root of the sample size

Standard Deviation of the population

• the SD can be with or without replacement

• with replacement will be the OG formula

• without replacement will be a diff formula

Sample Size and Sampling Error

• the larger the sample size the smaller the SD

• the smaller the SD the ore closely the possible values of xbar around the mean

• SD if often referred to as the Standard Error of the sample mean

Sampling Dist of the Sample Mean for Norm Dist variables

• if the variable under considertation is norm dist so is the variable Xbar

• suppose that a variable x of a populatioin is normally dist with mean and SD—> then for sample size n, the variable Xbar is also norm dist and has mean mu and SD small sigma/square root of n

Central Limit Theorem (CLT)

For a relatively large sample size, the variable Xbar is approx norm dist regardless of the dist of the variable under consideration (approx becomes better with increasing sample size)

• usually size of 30 or more is recommended