Calculating Two sample Paired/Dependent T test:

This is used to test the statistical difference between two means from two different populations.

     For example, a two-sample hypothesis could be used to test if there is a difference in the mean salary between male and female software engineers in the Bangalore area

    It is divided into two types.

1. Two sample paired T test
2. Two sample independent T test

Two sample paired T test

          Suppose sample of n players in a sports academy were asked to play before practice and after practice, Now we need to find out, in general if practice leads to improvement of players performance

Two sample independent T test

  Suppose that a sports academy has two buildings one for boys and other for girls.

Now head coach wants to know that boys and girls from different buildings are performing equally, In this case the head coach will pass instructions that girls and boys have to practice equally daily.

Now head coach wants to test whether the average number of hours practiced by boys is significantly different from the average for girls

Calculating Two sample Paired/Dependent T test:

Here we took two months sales details for one of the leading car vendor, now we want to check the Jan sales and feb sales are same.

Assumptions:

Step 1: Calculate the Mean for the difference between Jan and Feb Sales, Standard Deviation and Standard Error

Step 2: Lets Calculate the T value:

So T value is 2.812

In our case degree of freedom is 16 as we took the sample data with 17 observations, the degree of freedom will be n-1(17-1)

Step 3: Calculate P value:

As P value is close to 0.01 we can reject the Null hypothesis