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Introduction to Confidence Intervals definitions

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  • Confidence Interval
    A range of values constructed to likely contain a population parameter, offering more insight than a single estimate.
  • Population Parameter
    A fixed, usually unknown value that describes a characteristic of an entire group being studied.
  • Point Estimate
    A single value, such as x̄, used as the best guess for an unknown population parameter.
  • Confidence Level
    The probability, often expressed as a percentage, that a constructed interval contains the true parameter.
  • Alpha
    The probability that the true parameter falls outside the confidence interval, calculated as 1 minus the confidence level.
  • Margin of Error
    The maximum expected difference between a point estimate and the actual parameter, defining the interval's width.
  • Critical Value
    A z-score that marks the endpoints of a confidence interval, determined by the chosen confidence level.
  • Standard Normal Distribution
    A bell-shaped curve with mean zero and standard deviation one, used to find probabilities and z-scores.
  • Z Score
    A standardized value indicating how many standard deviations a point is from the mean in a normal distribution.
  • Endpoint
    A value at either extreme of a confidence interval, calculated by adding or subtracting the margin of error from the estimate.
  • Interval Notation
    A compact way to express a confidence interval using parentheses to show its lower and upper bounds.
  • Tail
    The area under the curve outside the confidence interval, representing the probability of extreme values.
  • Z Table
    A reference chart listing cumulative probabilities for standard normal z-scores, used to find critical values.
  • Complement
    The probability of all outcomes not included in a specified event, such as 1 minus the confidence level.
  • Y Hat
    A symbol representing the point estimate for a population parameter, often used in constructing intervals.