References: Introduction to the t Test ; t Test for a Single Sample ; t Test for Dependent Means

Introduction 18. Five sophomores were given an English achievement test before and after receiv- ing instruction in basic grammar. Their scores are shown below. Student Before After 20 18 18 22 M O Q O D 17 15 16 17 12 9 Is it reasonable to conclude that future students would show higher scores after instruc- tion? 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