Perform sign test on one-sample data, which is one of the oldest non-parametric statistical methods. Assume that X comes from a continuous distribution with median = v ( unknown ). Test the null hypothesis H0: median of X v = mu ( mu is the location parameter and is given in the test ) v.s. the alternative hypothesis H1: v > mu ( or v < mu or v != mu ) and calculate the p-value. When the sample size is large, perform the asymptotic sign test. In both ways, calculate the R-estimate of location of X and the distribution free confidence interval for mu.
