An equivalence between hypothesis tests and confidence intervals was demonstrated in chapter 9. In chapter 10, a nonparametric confidence interval for the median, n, was derived. Explain how to use this confidence interval to test the hypothesis Ho: n = n0. In the case where no= 0, show that using this approach on a sample of differences from a paired experiment is equivalent to the sign test. The sign test counts the number of positive differences and uses the fact that in the case that the null hypothesis is true, the distribution of the number of positive differences is binomial with (n, .5). Apply the sign test to the data from the measurement of mercury levels, listed in Section 11.3.3.

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