CH 7 Estimation/sampling distributions

are truly random samples really impossible?

true

what is the second characteristic of the central limit theorem

2) the standard error of the mean (SEM) decreases as the sample size increases and as variability of scores decreases

what is the a third characteristic of the central limit theorem

3) as the sample size increases, the shape of the distribution will approach normal.

Standard Error the Mean (SEM)

Is the average standard deviation of the sample means from the population mean.

As the sample size becomes larger, what happens to the distribution?

It reflects a more normal distribution

Are samples finite or infinite? what about populations?

Samples are finite, populations are infinite.

unbiased standard deviation

called the standard deviation estimate, is on avg., closer to the population standard deviation than the biased sample standard deviation

the sample mean is a more accurate estimator of the population mean when the SEM is what?

is small, rather than when it is large

A lower SEM value means what?

it is a better estimate of the population

sampling error

reflects the fact that a sample statistic may differ from the value of its corresponding population parameter, b/c it's based on a small portion of the overall population.

the sample mean differs from the population mean due to what?

sampling error

what is the best measure of the amount of sampling error associated with a sample mean?

standard error of the mean

what does the standard deviation of a set of raw scores represent?

the average deviation from the mean of the distribution

as the degrees of freedom increases, what happens?

the more accurate that statistic will be in estimating the corresponding population parameter.

the mean of a sampling distribution of the mean equals what?

the population mean

The SEM gets smaller as what two things happen?

the sample size increases, and the variability of scores decreases.

what is the standard deviation of a sampling distribution of the mean? and what does it represent?

the standard error of the mean, represents an average deviation of the sample means from the population mean

variance estimate

the unbiased estimator of the population variance, corrects the tendency of the sample variance to underestimate the population variance.

Can population parameters be estimated for all sizes of populations?

yes

unbiased estimator

a statistic whose average mean across samples equals the value of the parameter

central limit theorem

as the sample size increases, the distribution becomes normal and the standard error of the mean (SEM) closer to zero

why is the sample variance biased?

because it underestimates the population variance

biased standard deviation

called the sample standard deviation, is calculated from the biased sample variance.

What is the first characteristic of the central limit theorem

1) the mean of a sampling distribution of means will always be equal to the population mean.

what are the three characteristics of the central limit theorem

1) the mean of a sampling distribution of means will always be equal to the population mean. 2) the standard error of the mean (SEM) decreases as the sample size increases and as variability of scores decreases 3) as the sample size increases, the shape of the distribution will approach normal.

name 3 examples of unbiased estimators

1) the sample mean is an unbiased estimator of the population mean 2) variance estimate is an unbiased estimator of the population variance 3) standard deviation estimate is an unbiased estimator of the population standard deviation

2 factors that influence SEM

1- sample size 2- variability of scores in the population

What is typically the goal of research

To explain the behavior of large numbers of individuals