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6.5: Chapter 6 Key Terms

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    Confidence Interval (CI)
    an interval estimate for an unknown population parameter. This depends on:
    • the desired confidence level,
    • information that is known about the distribution (for example, known standard deviation),
    • the sample and its size.
    Confidence Level (CL)
    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.
    Degrees of Freedom (df)
    the number of objects in a sample that are free to vary
    Error Bound for a Population Mean (EBM)
    the margin of error; depends on the confidence level, sample size, and known or estimated population standard deviation.
    Error Bound for a Population Proportion (EBP)
    the margin of error; depends on the confidence level, the sample size, and the estimated (from the sample) proportion of successes.
    Inferential Statistics
    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.
    Normal Distribution
    notation: \(X \sim N(\mu,\sigma)\). If \(\mu = 0\) and \(\sigma = 1\), the RV is called the standard normal distribution.
    a numerical characteristic of a population
    Point Estimate
    a single number computed from a sample and used to estimate a population parameter
    Standard Deviation
    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
    Student's t-Distribution
    investigated and reported by William S. Gossett in 1908 and published under the pseudonym Student; the major characteristics of this random variable (\(RV\)) are:
    • It is continuous and assumes any real values.
    • The pdf is symmetrical about its mean of zero.
    • It approaches the standard normal distribution as \(n\) get larger.
    • 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.

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