Discussion
A manufacturer claims that the median lifetime of its product is more than 500 hours. To verify the claim based on 20 randomly observed lifetimes, which of the following tests is most appropriate ?
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.
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