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Chi Square Distribution quiz

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  • What type of distribution is used to construct confidence intervals for variance?
    The chi-square distribution is used to construct confidence intervals for variance.
  • Why can't you use the same critical value for both tails in the chi-square distribution?
    Because the chi-square distribution is asymmetric, you must find separate critical values for each tail.
  • What is the formula for degrees of freedom when using the chi-square distribution?
    Degrees of freedom are calculated as n - 1, where n is the sample size.
  • What is the range of possible values for the chi-square distribution?
    The chi-square distribution only takes positive values, starting at zero and extending to positive infinity.
  • How do you find the area to the right of the right-tail critical value in the chi-square table?
    You use alpha/2 as the area to the right of the right-tail critical value.
  • How do you find the area to the right of the left-tail critical value in the chi-square table?
    You use 1 - alpha/2 as the area to the right of the left-tail critical value.
  • What are the labels for the right and left critical values in the chi-square distribution?
    The right critical value is labeled as chi-square r, and the left as chi-square l.
  • For a 95% confidence interval with n = 31, what are the degrees of freedom?
    The degrees of freedom are 30, since 31 - 1 = 30.
  • What are the approximate critical values for a 95% confidence interval with n = 31?
    The critical values are approximately 16.79 (left) and 46.98 (right).
  • How do you calculate alpha for a 95% confidence interval?
    Alpha is calculated as 1 minus the confidence level, so alpha = 1 - 0.95 = 0.05.
  • What is the area used to find the right-tail critical value for a 95% confidence interval?
    The area is alpha/2, which is 0.025 for a 95% confidence interval.
  • What is the area used to find the left-tail critical value for a 95% confidence interval?
    The area is 1 - alpha/2, which is 0.975 for a 95% confidence interval.
  • Why can't you simply flip the sign of a chi-square critical value to find the other tail's value?
    Because the chi-square distribution is not symmetric, flipping the sign does not give the correct value.
  • When using a chi-square table, what two pieces of information do you need to find a critical value?
    You need the area to the right of the value and the degrees of freedom.
  • How are chi-square tables typically organized for finding critical values?
    Chi-square tables have areas to the right across the top row and degrees of freedom down the side.