A school conducted special classes to help students with poor verbal english. Each student

was required to give a test twice, once before starting the classes (Test 1) and once again after

completing 4 weeks in the class (Test 2).

Let Y1 and Y2 be the scores in Test 1 and Test 2 respectively.

Let Y = Y2 - Y1. Hence, if the population mean for Y is equal to zero, then the special classes

have no effect on the average.

It is planned to test the null hypothesis of the class having no effect, against the alternative

hypothesis that there is a positive effect due to the classes.

Student Test 1 Test 2

Abhay 5 8

Bhumika 3 10

Charan 2 5

Dinesh 4 7

Variable Number of

Students

Mean Standard

Deviation

Standard error

Y 4 4.000 2.000 1.000

a. Set up the null and alternative hypothesis

b. Are the classes beneficial to the students? Make a decision using Significance level as

0.05.

c. State whether the following statement is true or false:

When we make a decision using Significance level = 0.05, this means that the special

classes are truly beneficial, but there is a 5% chance that the classes are not beneficial