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Introduction to Confidence Intervals definitions

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  • Confidence Interval
    A range constructed around a point estimate, indicating where a parameter is likely to fall with a specified probability.
  • Parameter
    A value representing a characteristic of a population, often estimated using sample data.
  • Point Estimate
    A single value derived from sample data, used as the best guess for an unknown population parameter.
  • Margin of Error
    The maximum likely difference between a point estimate and the true parameter, defining the interval's width.
  • Confidence Level
    The probability that a constructed interval contains the true parameter, commonly expressed as a percentage.
  • Alpha
    The probability that the true parameter lies outside the confidence interval, calculated as 1 minus the confidence level.
  • Critical Value
    A threshold, often a z-score, marking the endpoints of a confidence interval based on the chosen confidence level.
  • Z-Score
    A standardized value indicating how many standard deviations a point is from the mean, used in interval calculations.
  • Standard Normal Distribution
    A symmetric, bell-shaped curve with mean zero and standard deviation one, underlying z-score calculations.
  • Endpoint
    A value marking the boundary of a confidence interval, calculated by adding or subtracting margin of error from the point estimate.
  • Tail Area
    The region under the curve outside the confidence interval, representing the probability of not containing the parameter.
  • Interval Notation
    A format expressing a confidence interval as two values in parentheses, denoting its lower and upper bounds.
  • Z Table
    A reference chart listing areas under the standard normal curve for various z-scores, used to find critical values.
  • Complement
    The portion of probability not included in the confidence level, represented by alpha in interval calculations.
  • Probability
    A measure quantifying the likelihood of an event, such as a parameter falling within a confidence interval.