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Confidence Interval (CI)
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an interval estimate for an unknown population parameter. This depends on:
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the desired confidence level,
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information that is known about the distribution (for example, known standard deviation),
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the sample and its size.
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Confidence Level (CL)
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the percent expression for the probability that the confidence interval contains the true population parameter; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter.
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Degrees of Freedom (
df
)
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the number of objects in a sample that are free to vary
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Error Bound for a Population Mean (EBM)
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the margin of error; depends on the confidence level, sample size, and known or estimated population standard deviation.
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Error Bound for a Population Proportion (EBP)
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the margin of error; depends on the confidence level, the sample size, and the estimated (from the sample) proportion of successes.
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Inferential Statistics
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also called statistical inference or inductive statistics; this facet of statistics deals with estimating a population parameter based on a sample statistic. For example, if four out of the 100 calculators sampled are defective we might infer that four percent of the production is defective.
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Normal Distribution
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notation: \(X \sim N(\mu,\sigma)\). If \(\mu = 0\) and \(\sigma = 1\), the RV is called
the standard normal distribution
.
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Parameter
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a numerical characteristic of a population
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Point Estimate
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a single number computed from a sample and used to estimate a population parameter
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Standard Deviation
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a number that is equal to the square root of the variance and measures how far data values are from their mean, on average; notation: \(s\) for sample standard deviation and \(\sigma\) for population standard deviation
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Student's
t-
Distribution
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investigated and reported by William S. Gossett in 1908 and published under the pseudonym Student; the major characteristics of this random variable (\(RV\)) are:
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It is continuous and assumes any real values.
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The pdf is symmetrical about its mean of zero.
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It approaches the standard normal distribution as \(n\) get larger.
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There is a "family" of
t
distributions: each representative of the family is completely defined by the number of degrees of freedom, which depends upon the application for which the t is being used.