Response to the following problem:
1. 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.