Chapter 7; Probability and Samples: The Distribution of Sample Means

A population has u= 60 with σ= 5; the distribution of sample means for samples of size n=4 selected from this population would have an expected value of.

60.

T or F: As sample size increases, the value of the standard error decreases.

True.

Standard Error of M

Variability of a distribution of scores is measured by the standard deviation. Variability of a distribution of sample means is measured bu the standard deviation of the sample means, and is called the standard error of M, σM. -aka SE standard error.

Given a random sample...

it is unlikely that the sample means would always be the same. * SAMPLE MEANS DIFFER FROM EACHOTHER.

A random sample of n =16 scores is obtained from a population with u= 5- and σ= 16. If the sample mean is M=58, the z-score corresponding to the sample mean is

z=2.00

z score for Sample Means

z=M - u/ σM.

t or f- A sample mean with z= 3 is a fairly typical score

f

The mean of the sample is always equal to the population mean

f. it will vary

Know this formula :

X- u/ σ/√n

Central Limit Theorem

*Distribution of a sample means approaches a normal distribution as n approaches infinity. *-Distribution of sample means for samples of size n will have a standard deviation= σ/√n

T or F: The shape of a Distribution of sample means is always normal

False.

Expected values of M

M is unbiased because expected value of distribution of sample-> value of population mean u. uM= u

Shape of the Distribution of Sample Means

The distribution of sample means is almost perfectly normal in either of two conditions 1. The population from which the samples are selected from is a normal distribution 2. The number of scores, n, in each sample is relatively large- at least 30.

Population variance

The smaller the variance in the population, the more probable it is that the sample mean will be close to the population mean.