List of top Statistics Questions on Testing of Hypothesis

A test which maximizes the power of the test for fixed size \(\alpha\) is called as :

The Neyman-Pearson Lemma can be used to test the hypothesis :

The degree of freedom for the statistic \(t\) for paired \(t\)-test based on \(n\) pairs of observations is :

Two samples are randomly selected from each population. The sample statistics are given below:

Use \(\alpha = 0.05\). \(n_1 = 50, \bar{x}_1 = 21, s_1 = 1.5\) and \(n_2 = 60, \bar{x}_2 = 19, s_2 = 1.9\).

What is the standardized test statistic to test the hypothesis that \(\mu_1 = \mu_2\)?