Chapter 7

standard error of M

*σM measure of how much difference/ distance is expected between a sample mean and population mean - decreases with bigger sample size (n=30) *describes variability of the distribution of sample means

describe the central tendency of the distribution of sample means

expected value of M

size of the sample influences:

how accurately the sample represents its population - a large sample would be more accurate - as the sample size increases, the error between the sample mean and the population mean should decrease

Which of the following would cause the standard error of M to get smaller?

increasing the sample size and decreasing the standard deviation

central limit theorem

mathematical proposition which serves as a cornerstone for much of inferential statistics - provides a precise description of the distribution that would be obtained if you selected every possible sample, calculated every sample mean, and constructed the distribution of the sample mean - distribution of sample means for sample size n will have M = μ and σ = σ/sqrrt(n) - will approach a normal distribution as n increases n>30

expected value of M

mean of the distribution of sample means which is always equal to the population mean - common sense - When all of the possible sample means are obtained, the average value is identical to μ, so μM=μ *describes central tendency of the distribution of sample means

sampling error

natural discrepancy between the mean for a sample and the mean for the population

standard error

provides a way to measure the "average," or standard, distance between a sample mean and the population mean - tells exactly how much error, on average, should exist between the sample mean and the unknown population mean - provides a method for defining and measuring sampling error

law of large numbers

rule that larger sample size increases probability that sample and population means will be close

central limit theorem describes the distribution of sample means by identifying the three basic characteristics that describe any distribution:

shape, central tendency, and variability

describe the variability of the distribution of sample means

standard error of M

sampling distribution

statistics obtained by selecting all possible samples of a specific size from a population - distribution of statistics

describe the shape of the distribution of sample means

this distribution is almost perfectly normal if either of the following two conditions is satisfied: - the population from which the samples are selected is a normal distribution - n>30

μM

used to represent the mean of the distribution of sample means and expected value of M but μM=μ

purposes for the standard error in the distribution of sample means

- the standard error describes the distribution of sample means. It provides a measure of how much difference is expected from one sample to another. When the standard error is small, all the sample means are close together and have similar values. If the standard error is large, the sample means are scattered over a wide range and there are big differences from one sample to another. - standard error measures how well an individual sample mean represents the entire distribution. Specifically, it provides a measure of how much distance is reasonable to expect between a sample mean and the overall mean for the distribution of sample means. However, because the overall mean is equal to μ, the standard error also provides a measure of how much distance to expect between a sample mean (M) and the population mean μ.

distribution of sample means

collection for all the possible random data sets of a particular size - contains all the possible samples

z=(M-μ)/σM

z-score for sample mean