A Paired T-Test takes the difference of the means from two samples and produces a t-value from this information. So basically a t-test will measure the difference between two samples. 

A t-test is variation of a hypothesis test. The first step in this test would be to state the null and alternate hypothesis. As this is a t-test the equations will be different.

null hypothesis: H ₀: μ         The null is stated as the average of the means or μ

alternative hypothesis: H _a : μ        The alternate hypothesis is the average of the means of what we are trying to prove  

The next step would be to check the conditions as we would in a normal hypothesis test however there is one different condition instead of success/failure we check the nearly normal condition, otherwise the other two conditions are the same. The next step you would take would be to calculate your t-value if you are doing it by hand for that you would use this equation. Otherwise you would compute your t-value using SPSS, the steps for that are listed below. 

t=y-/(s/n)  

Depending on results from your test you would either choose to reject the null value or if there is insufficient evidence then you would not reject the null value. 

 To conduct a Paired Sample T-Test in SPSS follow these simple steps:

Step 1: Go to the top of the screen and mouse over the word Analyze

Step 2: Scroll through the list and find Compare Means,  from this another menu drops down and you are going to select Paired Samples T-Test. 

Step 3: A menu will open with your data in a white box to the left, and another menu to drag and drop your variables into. With this menu open drag and drop the two variables you would like to compare in the same row. 

Step 4: Once you have done this you have the ability to go to the Options menu in the top right corner to change your Confidence interval Percentage. 

Step 5: Now that we have done everything, we are free to press OK and let SPSS perform the T-Test. SPSS should bring a new window displaying the results of the Sample T-Test. 

Congratulations you have completed a Paired Sample T-Test!