Hey guys, I'm really bad at statistics and maths in general and am stuck on a few questions. Any help is appreciated.

The information given with the question is:

"A researcher arguing for stricter laws for drink driving claims that even one glass of strong beer can produce a significant slowing of reaction time. I an attempt to prove her claim, she selects a random sample of 8 people
from the population and measures their baseline reaction times. This is accomplished by putting the subjects in a driving simulator. The subjects have to follow a car. One of the measures the simulator records is the time taken to apply the foot brake each time the brake lights of the car in front come on. The subjects then consume a glass of strong beer. 30 minutes later they are tested again. The median reaction times to respond to the break lights for each condition are shown below along with other information.

Median Reaction Times
(milliseconds):

Baseline | Beer
196.75 | 215.625

D = 18.875 (sample average)

Σd^2 = 5074.875

I've worked out that the estimated standard deviation of the population of difference scores is 26.925, and the estimated standard deviation of the distribution of the means of difference scores is 9.52.


How do I do THIS:

Adopting a significance or alpha level of 5% (.05 probability), what is the
two-tailed, critical or cut-off value of t for this study?

and THIS

What is the obtained value of t and would you retain or reject the null
hypothesis?


I know these are probably basic questions, but I'm stuck, and appreciate some guidance

Alright. Well, you did the hard part for me.

Alright, this is actually pretty simple. If your prof wants the "critical" value for a statistical test you look it up in a table of standard values. Since it asks for a t value (and the number of samples is extremely small), use the t table.

I get 1.415 if I remember correctly that df = n- 1.

Okay, well first we need to figure out what the null hypothesis IS. Since we're going for stricter drunk driving laws, I'm guessing that we're looking for a decreased reaction time. So the null hypothesis would be that there is no difference, or there is an increased reaction time (u <= 0 iff u = drunk - sober times). And our hypothesis would be that there is a decreased reaction time (u >= 0).

Since this is a t test we use the formula:

t = (d - u) / (s / root(n))

Where s is the sample standard deviation and n is the size of your sample (8). I noticed you were given/calculated the population standard deviation. This would be great if you were using a z test. Since you aren't, use the sample standard deviation ONLY.

If you input your numbers into there (remember u = 0 since
your null hypothesis predicts no difference or better) you get 5.608 (rounding to three decimal places).

In order to reject our null hypothesis we would have to have a t value greater than our critical t value of 1.415. It seems quite self-explanatory then that we reject our null hypothesis.

In conclusion; don't drink and drive.

(someone check this for me; I'm under-confident and always worried that I'm making a mistake even though I got an A in stats)

Thanks a lot for the help. I appreciate it. Pretty sure I did well on my exam