Following are interest rates (annual percentage rates) for a 30-year fixed-rate mortgage from a sample of lenders in Colorado on November 9, 2021. Assume that the population is normally distributed.

Construct a 95\% confidence interval for the population variance \(\sigma^{2}\).
The chi-square distribution is skewed, but as the number of degrees of freedom becomes large, the skewness diminishes. If the number of degrees of freedom, \(k\), is large enough, the chi-square distribution is reasonably well approximated by a normal distribution with mean \(k\) and variance \(2 k\).

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3.015 2.891 2.875 3.163 3.275 2.934 3.417 3.124 3.145 3.011 3.009 3.375