Suppose a sample of 30 students were given a diagnostic test before studying a particular module and then again after completing the module. We want to find out if, in general, our teaching leads to improvements in students’ knowledge/skills (i.e. test scores). Let y = test score after the module, and x  = test score before the module. (di=yi−xi).   d¯=1.05 sd=2.837      At the 5% significance level, do the data provide sufficient evidence to conclude that the module leads to improved test scores? State the null and alternative hypotheses. H0: _________________                       Ha:_______________________

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.