Chi-Squared confidence intervals - Confidence Intervals

Chi-Squared confidence intervals


To estimate a population variance a Chi-Squared distribution is used,
• Chi-Squared: X2=(n1)s2σ2X^2=\frac{(n-1)s^2}{\sigma ^2}
nn: sample size
ss: sample standard deviation
σ\sigma: population standard deviation
(n1)(n-1): is also called "degrees of freedom"
• Chi-Square table gives critical value area to the right

The Confidence interval for the variance is given by:
(n1)s2XR2\frac{(n-1)s^2}{X_R^2} < σ2\sigma ^2 < (n1)s2XL2\frac{(n-1)s^2}{X_L^2}
  • 1.
    Determining Degrees of Freedom
    How many degrees of freedom does a sample of size,
  • 2.
    Determining the Critical Value for a Chi-Square Distribution (XR2(X_R^2 and XL2)X_L^2)
    If a Chi-Squared distribution has 8 degrees of freedom find XR2X_R^2 and XL2X_L^2, with a
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Chi-Squared confidence intervals

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