Question

Twenty college students experience the effects of alcohol on reaction time. They perform very basic timed responses in a driving simulator both before and after consuming several alcoholic beverages. The researcher collects a reaction-time result for each of the 20 students before and after intoxication, for a total of 40 measures. What is the null hypothesis for this paired-samples study?

Answer 1

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:
`\mu_y- \mu_x \leq 0`

Alternative hypothesis:
`\mu_y -\mu_x >0`

We can define the difference as:
`d_i=y_i-x_i`

And the system of hypothesis are:

Null hypothesis:
`\mu_d \leq 0`

Alternative hypothesis:
`\mu_d >0`

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:
`\mu_y- \mu_x \leq 0`

Alternative hypothesis:
`\mu_y -\mu_x >0`

We can define the difference as:
`d_i=y_i-x_i`

And the system of hypothesis are:

Null hypothesis:
`\mu_d \leq 0`

Alternative hypothesis:
`\mu_d >0`