We help IT Professionals succeed at work.

using t test to compare sample mean to population mean

andieje asked
Medium Priority
Last Modified: 2012-08-13
I am new to statistics to please bear with me.

I am using a t test to compare a sample mean to a population mean (it's a question in a book). The t test gives a vaslue of 2.536. This gives a two tailed probability of
0.02 <p <0.05

and a one tailed probability of
0.1 < p< 0.025

The two tailed probability is double the one tailed probability. This doesnt make sense to me. Shouldn't it be the other way around.

Please can you clarify for me

Watch Question

No it is just right. Each tail is similar to the other. If you have a 5% possibility to be in one tail you have a 5% probability to be in the other tail too. Total 10% probability

Not the solution you were looking for? Getting a personalized solution is easy.

Ask the Experts
Remember that p is the probability of obtaining a t of 2.536 or greater just by chance alone (i.e., not because your sample is actually different from the population).

If you're doing a one-tailed test, p is the probability of getting a result just in the one tail you're interested in. If you're only interested in really high scores, you care about the p of t >= 2.536, and if it's really low scores, it's p of t <= -2.536. Either way, in your case, p is between 0.01 and 0.025.

If you're doing a two-tailed test, p is the probability of getting EITHER t >= 2.536 OR t <= -2.536 just by chance alone. If your sample truly is random and there's nothing special about it, there's an equal chance of it being in the extreme of either tail. Thus the probability of it being in one tail OR the other is double the probability of it being in one particular tail.
Maybe you're confused because you're thinking of the critical region, which is distinct from p.

First, define alpha as the risk of a type I error. This is something you decide. Say you will accept alpha = .05.

Next you decide if you want a 1 tailed or 2 tailed test. If it's one tailed, the entire .05 is in one side of the distribution. If it's two tailed, alpha is split in 2, with .025  on the left and .025 on the right. But alpha is still .05.

Thus you have an idea in your mind that a two tailed test has a smaller "p-value" but what's small is the size of the rejection region which is alpha/2. A two tailed test has a smaller critical rejection region on each side of the distribution.

The other commenters have it right when they're explaining why the p-value is larger for 2 tailed.

What I'm pointing out is why you are surprised by the fact that a 2-tailed p is larger. I think you're surprised because you're imaging the distribution with alpha/2 critical regions on each side of the curve, and you're thinking "smaller." But those are not p-values. Those are components of alpha.


hi, all of your answers were useful. The problem was simply that I had confused myself because of something I had read in a badly written book. I will split the points




by the way jtm11, you were right in seeing how I had confused myself. Very intuitive
Access more of Experts Exchange with a free account
Thanks for using Experts Exchange.

Create a free account to continue.

Limited access with a free account allows you to:

  • View three pieces of content (articles, solutions, posts, and videos)
  • Ask the experts questions (counted toward content limit)
  • Customize your dashboard and profile

*This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.


Please enter a first name

Please enter a last name

8+ characters (letters, numbers, and a symbol)

By clicking, you agree to the Terms of Use and Privacy Policy.