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Chapter 7 - Coggle Diagram
Chapter 7
shape
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this distribution is almost perfectly normal if either of the following two conditions is satisfied 1. population from which the samples are selected is a normal distribution. 2. number of scores (n) in each sample is relatively large, around 30 or more.
n gets larger, the distribution of sample means will closely approximate a normal distribution
when you take lots of different samples, you expect the sample means to “pile up” around m, resulting in a normal-shaped distribution
standard error of M
standard deviation of the distribution of sample means, σM
provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (μ)
always is some discrepancy or error between a sample statistic and the corresponding population parameter
for any sample size (n), we can compute the standard error, which measures the average distance between a sample mean and the population mean
magnitude of the standard error is determined by two factors: (1) the size of the sample and (2) the standard deviation of the population from which the sample is selected
law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean
bigger samples have smaller error, and smaller samples have bigger error
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characteristics
sample means should pile up around the population mean. Samples are not expected to be perfect but they are representative of the population. As a result, most of the sample means should be relatively close to the population mean
pile of sample means should tend to form a normal-shaped distribution. Logically, most of the samples should have means close to μ, and it should be relatively rare to find sample means that are substantially different from μ. As a result, the sample means should pile up in the center of the distribution (around μ) and the frequencies should taper off as the distance between M and μ increases. This describes a normal-shaped distribution
the larger the sample size, the closer the sample means should be to the population mean, μ. Logically, a large sample should be better than a small sample because it is more representative. Thus, the sample means obtained with a large sample size should cluster relatively close to the population mean; the means obtained from small samples should be more widely scattered
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central limit theorum
or any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of σ and will approach a normal distribution as n approaches infinity
describes the distribution of sample means by identifying the three basic characteristics that describe any distribution: shape, central tendency, and variability
mean
when you take lots of different samples, you expect the sample means to “pile up” around m, resulting in a normal-shaped distribution
expected value of M
mean of the distribution of sample means is equal to the mean of the population of scores, μ, and is called
whenever you have a probability question about a sample mean, you must use the distribution of sample means
z-scores
the sign tells whether the sample mean is located above (+) or below (−) the mean for the distribution
the number tells the distance between the sample mean and μ in terms of the number of standard errors
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
you are working with a sample mean, you must use the standard error!!!!
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sampling error
the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
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