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Chapter 7: Probability and Samples. Introduction of the distribution of…
Chapter 7: Probability and Samples. Introduction of the distribution of sample means which tends to be normal; we are able to find probabilities using z-score and the unit normal table
Difference or Error
Sampling error is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter. Samples are variable and are not all the same (like you and me)
Distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population. Contains ALL the possible samples.
Sampling distribution or sampling distribution of M is a distribution of statistics obtained by selecting all the possible samples of a specific size from a population
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Shape
Central limit theorem specifies the shape, central tendency, and variability for the distribution of sample means
Value of this theorem is that it describes the distribution of sample means for any population and it approaches a normal distribution very rapidly
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Variability: standard error of M working with the standard deviation of the sample means. The standard deviation is called the standard of error
Describes the distribution of sample means and measures of how much difference is expected from on sample to another
Measures how well and individual sample mean represents the entire population. Providing a measure of how much distance is reasonable to expect between a sample mean and overall mean for the distribution sample means.
Shape: perfectly normal when n> 30, the distribution is normal regardless of the shape of the original population
Size
Large sample is more accurate than small sample according to the low of large numbers. As the sample size increases, the error between the sample mean and the population mean should decrease.
Location
Z-score is used to describe the exact location of any specific sample mean within the distribution of sample means. It tells whether the location is above (+) or below (-) the mean and the number tells the distance between the location and the mean in terms of standard deviations