Five sophomores were given an english achievement test before and

     Five   sophomores were given an English achievement test before and after   receiving instruction in basic grammar.   Their scores are shown below.   Student Before After   A 20 18   B 18 22   C 17 15   D 16 17   E 12 9   Is it reasonable to conclude that future   students would show higher scores after   instruction? Use the .05 significance   level. (a) Use the steps of hypothesis testing.   (b) Sketch the distributions involved (c)   Explain your answer to someone   who understands mean, standard deviation,   and variance but knows nothing else   about statistics.    

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