The Student T-Test (Two tailed)

[Mykester]

My bio teacher is basically a dumbass. He doesn't teach us anything (literally) and gives us a test. Just yesterday we had to do a lab for him and we had no outline, (just said look at your handout, and I see that I have 20, with a rat on it and showing me how to make a graph on excel, real useful if I don't know what I'm doing).

But that aside, I don't understand the student's t test. What is the point of it? I have all the equations memorized for things like standard deviation, standard error, freedom (lol), variance, etc. How the hell do I make one? I'm looking at the sheet and I'm basically just going wtf. Like I just want a basic run down of it. I found out how to find the valus on my graphing calculator. That's nifty and all, but I don't understand how on the sheet, there are different values for each df. All I got was one df and on p, and we're probably going to have to make a t tailed table on tomorrow's test.

 

[statdad]

I'll ignore the assertions based on opinion.

If you are referring to a one-sample t-test, it is used in the process of testing a hypothesis about the size of a population mean (mean birth-weight of a rat, mean brain size, mean of any numerical quantity).

If you've seen a one-sample Z-test statistic

$$Z = \frac{\bar X - \mu_0}{\dfrac{\sigma}{\sqrt{n}}}$$

you know that when you discuss rejection regions a single value from the standard normal distribution can be used to mark the boundary of that rejection region, regardless of the sample size.
When you calculate a $$t$$-statistic

$$t = \frac{\bar X - \mu_0}{\dfrac{s}{\sqrt{n}}}$$

construction of a rejection region is slightly more complicated. The short story: you need a different value from a $$t$$-distribution for each sample size. The appropriate distribution is determined by the degrees of freedom (not simply freedom):

$$d.f. = n - 1$$

This is why there are different values on your sheet.
To do a $$t$$-test:

1. Write out your hypotheses (should be done before the experiment in which data are gathered)
2. Determine your desired level fo significance level (again, before the experiment)
3. Calculate the rejection region - cutoffs come from the appropriate $$t$$-distribution
4. Make the decision

 

[Focus]

statdad forgot to mention (but implied) that the mean is unknown when you use a t-test. To sum it up, you use a t-test to test hypotheses about the mean of a sample when you do not know the variance.

 

[rbeale98]

to understand the t-test it helps to first understand the z-test and that as df goes to infinity, t-value approaches z-value

 

[statdad]

Regarding
"statdad forgot to mention (but implied) that the mean is unknown when you use a t-test. To sum it up, you use a t-test to test hypotheses about the mean of a sample when you do not know the variance."

Partly correct when I stated that the $$t$$ test is used to to test for the value of the mean, I assumed (fairly/unfairly, but still an assumption I shouldn't have made) that the OP knew that the true value of $$\mu$$ was unknown.

but the second part of focus' quote contains a typographical error: the hypotheses are not about the mean of the sample - that is known - the test is about the size of the population mean . The sample mean is used in the work.

 

[Focus]

Regarding
"statdad forgot to mention (but implied) that the mean is unknown when you use a t-test. To sum it up, you use a t-test to test hypotheses about the mean of a sample when you do not know the variance."

Partly correct when I stated that the $$t$$ test is used to to test for the value of the mean, I assumed (fairly/unfairly, but still an assumption I shouldn't have made) that the OP knew that the true value of $$\mu$$ was unknown.

but the second part of focus' quote contains a typographical error: the hypotheses are not about the mean of the sample - that is known - the test is about the size of the population mean . The sample mean is used in the work.

Yes. And I meant that the variance is unknown. You don't need a t-test if you know the variance. Long day yesterday :zzz: