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Confidence Intervals for Population Variance definitions

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  • Confidence Interval
    A range of values calculated from sample data, within which the true population parameter is expected to fall with a specified probability.
  • Population Variance
    A measure of how data points in an entire group are spread out from their mean, estimated using sample data.
  • Standard Deviation
    The square root of variance, representing average distance of data points from the mean in a dataset.
  • Chi-Square Distribution
    A probability distribution used to estimate population variance from sample variance, especially for non-symmetric data.
  • Critical Value
    A cutoff point 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 select the correct row in the chi-square table.
  • Sample Variance
    A point estimate of population variance, calculated from the squared differences between sample data and their mean.
  • Lower Bound
    The smallest value in a confidence interval, found using the higher chi-square critical value in the denominator.
  • Upper Bound
    The largest value in a confidence interval, found using the lower chi-square critical value in the denominator.
  • Alpha
    The probability of error, found by subtracting the confidence level from one, then split to find critical values.
  • Chi-Square Table
    A reference chart used to look up critical values based on degrees of freedom and probability areas.
  • Point Estimate
    A single value derived from sample data, serving as the best guess for an unknown population parameter.
  • Confidence Level
    The probability that the calculated confidence interval contains the true population parameter, often expressed as a percentage.
  • Bracket Notation
    A way to express a confidence interval by listing the lower and upper bounds within brackets.
  • Normal Distribution
    A symmetric, bell-shaped distribution required for valid confidence interval calculations for variance.