Please enable JavaScript.
Coggle requires JavaScript to display documents.
PROBABILITY AND SAMPLES:
The objective is to describe the logically…
PROBABILITY AND SAMPLES:
The objective is to describe the logically predictable characteristics of the distribution, and use this information to determine characteristics of the distribution of sample means for a specific population and sample size.
SAMPLING ERROR: the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.
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.
SAMPLING DISTRIBUTION:
a distribution of statistics obtained by selecting all the possible samples of a specific size from a population.
-
SAMPLES: samples are variable, they are not the same
DISTRIBUTION CHARACTERISTICS:
The sample means should pile up around the population mean, the pile of sample means should tend to form a normal-shaped distribution, and the larger the sample size, the closer the sample means should be to the population mean.
CENTRAL LIMIT THEOREM: for 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.
FIRST VALUE OF THE THEOREM:
It describes the distribution of sample means for any population, no matter what shape, mean, or standard deviation
SECOND VALUE OF THE THEOREM:
the distribution of sample means “approaches” a normal distribution very rapidly. By the time the sample size reaches , the distribution is almost perfectly normal.
ONE PARAMETER OF THE DISTRIBUTION OF SAMPLE MEANS: Central Tendency - the mean of the distribution of sample means is identical to the mean of the population from which the samples are selected.
MEAN OF DISTRIBUTION OF SAMPE MEANS:
the average value of sample means is exactly equal to the value of the population mean
EXPECTED VALUE OF M:
The mean of the distribution of sample means is equal to the mean of the population of scores, μ
-
THREE DIFFERENT BUT INTERRELATED DISTRIBUTIONS: original population of scores, sample selected from population, and distribution of sample means.
Z-SCORE:*
tells exactly where the sample mean is located in relation to all the other possible sample means that could have been obtained.
Z-SCORE SIGN:
tells whether the sample mean is located above (+) or below (−) the mean for the distribution (which is the population mean, μ).
Z-SCORE NUMBER:
tells the distance between the sample and μ in terms of the number of standard errors
STANDARD ERROR:
provides a way to measure the “average,” or standard, distance between a sample mean and the population mean
TWO WAYS TO RECORD STANDARD ERROR MEAN:
it may be reported in a table along with the sample means or in graphs.