Question

Does a statistics course improve a student's mathematics skills,as measured by a national test? Suppose a random sample of 13 students takes the same national mathematics exam prior to enrolling in a stats course and just after completing the course. At a 1% level of significance determine whether the scores after the stats course are significantly higher than the scores before. Take the differences = before - after.

Before    After
430        465
485        475
520        535
360        410
440        425
500        505
425        450
470        480
515        520
430        430
450        460
495        500
540        530

Locate student 9 in the dataset. What rank will be given to this student? ________.


What is the value of the test statistic, T? Give answer to 1 decimal place. ________.


What is the critical value for the study? (Hint: student 10 will be dropped from the analysis, since the scores are the same before and after the stats class). ________.

Answer 1

As we are given the data of before treatment and after treatment, appropriate test will be paired t test.

To test, H0 : treatment is effective

against, H1 : treatment is not effective

Let d = before treatment - after treatment.

Then the values of d are;

Student number	d
1	-35
2	10
3	-15
4	-50
5	15
6	-5
7	-25
8	-10
9	-5
10	0
11	-10
12	-5
13	10

then, mean of d is given by,

and variance is given by,

then test statistic is given by,

Here, n = 13

then the value of test statistic is given by,

At 1% level of significance, tabulated value of t is given by,

Since, cat t < tab t,

Accept H0 at 1% level of significance

Treament is effective.

Assigning ranks to the d, we get the rank of 9th student is 8.