Question
State whether the following statements are True or False. Give reasons in support of your answer:
(i) When the population distribution is unknown and the data are measured on a nominal scale, the Sign test can be used to test a hypothesis about the median.
(ii) In the Bayesian framework, prior information about the parameter is combined with the likelihood to obtain the posterior distribution.
(iii) The Wilcoxon rank-sum test is a non-parametric alternative to the two-sample t-test when normality is not assumed.
(iv) A complete sufficient statistic guarantees the uniqueness of the unbiased estimator obtained through it.
(v) The power of a statistical test is the probability of accepting the null hypothesis when it is true.
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(i) False. The Sign test is a non-parametric test used to make inferences about the median, but it requires at least ordinal data so that observations can be meaningfully compared as being above or below the hypothesized median. Nominal scale data lack any inherent ordering, so it is not possible to determine signs relative to a median. Therefore, the Sign test cannot be appropriately applied when data are purely nominal. (ii) True. In the Bayesian framework, inference is based on updating prior beliefs about a parameter using observed data. This is done through Bayes’ theorem, where the prior distribution is combined with the likelihood function derived from the data to produce the posterior distribution. The posterior distribution
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