Following are interest rates (annual percentage rates) for a 30-year fixed-rate mortgage from a sample of lenders in Colorado on May 3, 2013. Assume that the population is normally distributed.

Construct a 95% confidence interval for the population variance σ².

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 2k.

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3.540 3.547 3.500 3.625 3.516 3.395 3.638 3.500 3.499 3.401 3.625 3.667