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Confidence Intervals for Population Variance definitions

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  • Confidence Interval
    A range of values calculated from sample data that likely contains the true population parameter with a specified probability.
  • Population Variance
    A measure of how data points in a population are spread out, estimated using sample variance and chi-square methods.
  • Standard Deviation
    A statistic representing the average distance of data points from the mean, found by taking the square root of variance.
  • Chi-Square Distribution
    An asymmetrical probability distribution used to construct intervals for variance and standard deviation.
  • Critical Value
    A threshold from the chi-square table that determines the bounds of a confidence interval for variance.
  • Degrees of Freedom
    A value calculated as sample size minus one, used to locate critical values in the chi-square table.
  • Sample Variance
    A point estimate for population variance, calculated from sample data and used in confidence interval formulas.
  • Chi-Square Table
    A reference chart listing critical values for the chi-square distribution based on degrees of freedom and area.
  • Lower Bound
    The smallest value in a confidence interval, calculated using the higher chi-square critical value in the denominator.
  • Upper Bound
    The largest value in a confidence interval, calculated using the lower chi-square critical value in the denominator.
  • Point Estimate
    A single value derived from sample data that serves as the best guess for a population parameter.
  • Confidence Level
    The probability that the constructed interval contains the true population parameter, often expressed as a percentage.
  • Alpha
    The complement of the confidence level, representing the total probability outside the interval.
  • Bracket Notation
    A format for expressing confidence intervals, showing the lower and upper bounds as a pair of values.
  • Normal Distribution
    A symmetric, bell-shaped distribution required for valid confidence interval calculations for variance.