2x^2-12x-16=0 solve by completing the square

For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:

The system of hypothesis for this case are:

Null hypothesis:

Alternative hypothesis:

We can define the difference as:  

And the system of hypothesis are:

Null hypothesis:

Alternative hypothesis:

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

x=test value before , y = test value after

Solution to the problem

For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:

The system of hypothesis for this case are:

Null hypothesis:

Alternative hypothesis:

We can define the difference as:  

And the system of hypothesis are:

Null hypothesis:

Alternative hypothesis: