Q1. 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.