Nonparametric Methods Questions and Answers

Answer: A

The most appropriate test is the sign test.

The claim concerns the median of a single population, with no assumption about the shape of the lifetime distribution. The sign test counts how many of the 20 lifetimes exceed 500 hours; under \(H_{0}\): median = 500, that count is Binomial(20, ½), so the test needs only the signs of the differences.

The Mann-Whitney test compares two independent samples. The Kolmogorov-Smirnov test compares whole distributions, not a median. The chi-square test is for goodness of fit or contingency tables and needs grouped counts.

Answer: B

The non-parametric analogue of the chi-square goodness-of-fit test is the Kolmogorov-Smirnov test.

Both test whether a sample comes from a specified distribution. The one-sample Kolmogorov-Smirnov statistic is the largest gap between the empirical distribution function and the hypothesised distribution function, \(D_{n} = \sup_{x} |F_{n}(x) - F_{0}(x)|\), and it works with ungrouped data.

The Mann-Whitney and median tests compare two samples' locations, and the Wilcoxon (signed-rank) test is about a location or paired difference; none of them tests goodness of fit to a given distribution.