Question

In this example (Shier 2004) we are going to suppose that we have a group of 11 students and we want to investigate the effect of the use of some didactic resource, for example a video on YouTube, in their ability to solve certain types of mathematical problems. We take an initial test (diagnosis), we ask them to watch the video and when they finish we take another test. We now have two observations from each student. We calculate the difference between them. The result of all this is summarized in the following table:

Table: Results of two math tests

Name

Before

Then

Luis

18

22

Javier

twenty-one

25

Pedro

16

17

Loneliness

22

24

Manuel

19

16

Cecilia

24

29

Cristina

17

twenty

Angel

twenty-one

2. 3

Manuela

2. 3

19

José

18

twenty

Juan

14

fifteen

 

 Establish the correct hypotheses and test. (20 pts)

Answer 1

The gains in results of two math tests (di) for the 11 students are:

4 , 4 , 1 , 2 , -3 , 5 , 3 , 2 , -4 , 2 , 1 .

It is assumed that the distribution of differences is continuous in the vicinity of its median .

We have to test,

(Paired-sample sign test)

There are 9 positive values among 11 non-zero values.

Under the null hypothesis, the expected no. of positive values among the dis in a sample of 11 pair is 5.5.

The sampling distribution of the no. of positive values follows the Binomial distribution with probability of a positive value = 0.5.

From the table of cumulative binomial probabilities, P(no. of positive values 9) = 0.033

So, the null hypothesis is accepted at 5% level of significance i.e. there are not enough evidance to reject null hypothesis.