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Confidence Intervals for Population Variance quiz

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  • What distribution is used to build confidence intervals for population variance?
    The chi-square distribution is used to build confidence intervals for population variance.
  • What is the point estimate when constructing a confidence interval for variance?
    The point estimate is the sample variance, denoted as s^2.
  • How do you calculate the degrees of freedom for a confidence interval for variance?
    Degrees of freedom are calculated as n - 1, where n is the sample size.
  • What are the critical values needed from the chi-square distribution to build the interval?
    You need two critical values: chi-square right (χ²r) and chi-square left (χ²l).
  • How do you find the alpha value for a 90% confidence interval?
    Alpha is found by subtracting the confidence level from 1, so alpha = 1 - 0.9 = 0.1.
  • What values do you use to look up the critical values in the chi-square table?
    You use alpha/2 and 1 - alpha/2 along with the degrees of freedom to look up the critical values.
  • What is the formula for the lower bound of the confidence interval for variance?
    Lower bound = (n-1)s^2 / χ²r.
  • What is the formula for the upper bound of the confidence interval for variance?
    Upper bound = (n-1)s^2 / χ²l.
  • Why does the higher chi-square critical value go in the denominator for the lower bound?
    Using the higher chi-square value in the denominator results in a smaller lower bound.
  • What assumption must be met to use this method for confidence intervals for variance?
    The sample must come from a normally distributed population.
  • How do you express the confidence interval for variance in bracket notation?
    You write the interval as [lower bound, upper bound].
  • How do you construct a confidence interval for standard deviation from the variance interval?
    Take the square root of both the lower and upper bounds of the variance interval.
  • What sample statistics are needed to build the confidence interval for variance?
    You need the sample size (n) and the sample variance (s^2).
  • What does a 90% confidence interval for variance mean in practical terms?
    It means you are 90% certain the true population variance lies within the calculated interval.
  • What is the main difference between confidence intervals for means and for variance?
    Confidence intervals for variance use the chi-square distribution and do not use a margin of error equation.