I. Problem : Non -parametric Sign Test The validity of the T-test relies heavily on the assumption that the sample X, ..., X is comprised of independent normal random variables . This is because only under this assumption d does the T- statistic follow a T-distribution . This assumption may often be safely made , however in certain cases we cannot assume a normal population and we need an alternative test . Here we present a particular type of non -parametric test known as the sign test . The phrase " non - parametric " implies that the distribution of the test statistic does not depend on any particular distributional assumption for the population . For the sign test , we begin by denoting the random variables x* = [ 1{X ; > up) a?d X" = [ 1{ X ; Mo) = P(X, u)