(Chapter 7: Distribution of Sample Means)

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 by the standard deviation of the sample means = standard error of M written as σM

factors that affect standard error

1) standard deviation from the population mean 2) the size of the sample

what is the probability of getting a number greater then 7 with n+16 scores

1/16

true

Central limit theorem describes the distribution of sample means by identifying the 3 characteristics that describe a distribution. Shape Central tendency and variability.

true

Distribution of sample means approaches a normal distribution as n approaches infinity -will have a mean of μM (mean of the means) -will have a standard deviation σM o/square root of n

Central Limit Theorem

If you make a sampling distribution from sample means for any population with a mean μ and a standard deviation σ... 1) the means of the sampling distribution will be the same as the population mean 2) the standard error will equal σ / square root of n 3) the means of the sampling distribution will approach a normal distribution

Probability

Primary use = find the probability associated with any particular sample (sample mean) •Proportions of the normal curve are used to represent probabilities •A z-score for the sample mean is computed

fact

Researchers typically want to study entire samples rather than single scores Sample provides estimate of the population (statistic estimate parameters)

Inferetial stats

Sample information is not a perfectly accurate reflection of its population (sampling error) •Differences between sample & population introduce uncertainty into inferential processes• Use probabilistic to draw inferences from sample data

shape of distribution of means

Shape is almost perfectly normal in either of 2 conditions: 1.The population from which the samples are selected is a normal distribution. or 2. The number of scores (n) in each sample is relatively large (at least 30).

Zscores for mean

Sign = location is above (+) or below (-) mean •Number tells average distance between mean of sampling distribution & population mean

True

T/F the value of the centeral theorem describes the distribution of sample means for any population, no matter what shape, mean or standard deviation. Second the distribution of sample means "approaches" a normal distribution very fast.

characteristics of Distribution of sample means

The sample means should pile up aroun the population mean The pile means should make a normal shaped distribution The larger the sample size the closer the sample mean should be to population mean u

sampling distribution

a distribution of all means obtained by selecting all possible random samples of a specific size (n) from a population

distribution of sample means

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

sample distribution

the distribution of all x values in a sample

Expected value of mean

the mean of the distribution of sample means is equal to the mean of the population of scores, u M is an unbiased statistic because μM = value of the population mean μ

law of large numbers

the principle that larger sample sizes more accurately represent the population and cause Ms to be closer to μ, while small sample sizes increase the likelihood of extreme outliers

standard error

the standard deviation of sample means; measures how far a typical sample mean (M) falls from the population mean (μ) determined by the following formula: σ / square root of n

standard error of M

the standard deviation of the distribution of sample means; provides a measure of how much distance is expected on average between a sample mean and the population mean

reason for distribution of sample means

to get an accurate sample equal to population

sampling error

when a sample is not representative of the population, which makes it impossible to make reasonable inferences about the population based off of the sample

the difference between standard error and standard deviation

while _________ measures how much sample means differ from a population mean, ________ measures how far the typical raw score falls from other raw scores

the difference between a sample distribution and a sampling distribution

while a _____________ distribution consists of all x values in a sample, a ____________ distribution consists of all sample means in a population

How are z-scores used to answer probability questions about sample means?

z-scores can be used to measure the probability of selecting a sample with specific characteristics from the population. In this way, we can determine whether an experiment allows accurate inferences about the population to be made.