Suppose a sample of n students were given a diagnostic test before studying a particular module and then again after completing the module. We want to find out if, our teaching leads to improvement in students test score. Student Pre-module score Post-module score Difference 1 18 22 4 2 21 25 4 3 16 17 1 4 22 24 2 5 19 16 -3 6 24 29 5 7 17 20 3 8 21 23 2 9 23 19 -4 10 18 20 2 11 14 15 1 12 16 15 -1 13 16 18 2 14 19 26 7 15 18 18 0 16 20 24 4 17 12 18 6 18 22 25 3 19 15 19 4 20 17 16 -1 a) Construct the null and alternative hypothesis. b) Calculate the t value using appropriate formula. c) Perform the paired t-test in statistical analysis software. d) State the conclusion.

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A: frequency distribution

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