A new prep class was designed to improve AP statistics test

A new prep class was designed to improve AP statistics test scores. Five students were selected at random. The numbers of correct answers on two practice exams were recorded; one before the class and one after. The data recorded in the table below. We want to test if the numbers of correct answers, on average, are higher after the class. Number of Correct Answers

Subject

Before the class

After the class

1

12

14

2

15

18

3

9

11

4

12

10

5

12

12

Solution

Let mu_d be the mean difference between Before the class and After the class

The test hypothesis:

Ho: mu_d =0 (i.e. null hypothesis)

Ha: mu_d<0 (i.e. alternative hypothesis)

The test statistic is

t= mean difference/(s/vn)

=-1/(2/sqrt(5))

=-1.118

The p-value= 0.16308 (from student t table)

Assume that the significant level a=0.05

Since the p-value is larger than 0.05, we do not reject Ho.

So we can not conclude that the numbers of correct answers, on average, are higher after the class.