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Chap 7: Probability and Samples: the Distribution of Sample Means - Coggle…
Chap 7: Probability and Samples: the Distribution of Sample Means
sampling error: natural discrepancy, or amount of error, between a sample stat and its corresponding population parameter
samples are variable but they are not all the same
different samples will all look different
distribution of sample means is the collection of sample means for all possible random samples obtain from a pop
sampling distribution is a distribution of statistics obtained by selecting all the possible samples of a specific size from a pop
so distribution of sample means is an
example
of a sampling distribution
to calculate you need the sample mean, and place the sample mean in a frequency distribution
large sample will be best!
central limit theorem
describes the distribution of sample means for any pop and "approaches" a normal distribution very rapidly
mean value
it's called the
expected value of M
biased vs unbiased
standard error of M: provides a measure of how much distance is expected on average between a sample and a population mean
extremely valuable measure because it specifies precisely how well a sample mean estimates its population mean
as sample size increases the error between the sample mean and the pop mean should decrease:
law of large numbers
z-score
Caution: When computing z for a single score, use the standard deviation, σ. When computing z for a sample mean, you must use the standard error σM
adjustments: using distribution of sample means instead of a distribution of scores and using standard error instead of standard deviation
another important rule: whenever you are working with a sample mean, you must use the standard error!
inferential statistics are methods that use sample data as the basis for drawing general conclusions about populations
sample is not an accurate reflection of its pop
must consider the margin of error
