# Thread: One sample t test with interval values

1. ## One sample t test with interval values

Hi everybody,

I fear this is going to be a dumb question.

I got some data where the possible values are restricted by an interval.

Specifically, even before my experiment started I knew that each observation would give ma a data point somewhere in the interval between 0 and 10, i.e., I knew that 0 was the smallest possible value. Actually, my hypothesis was "mean = 0"

I thought about performing a standard t test for my data with H0 being: "mean = 0" and H1 "mean value > 0". Now, a friend of mine laughed about this approach mumbling something like "you can't for a mean equal to an interval bound". Is he right? Obviously, i can not assume a normal distribution, but does this matter for n > 30?

Even if a t test isn't possible: Is there a general problem with testing for the smallest possible value - even for nonparametric tests?

Best regards,

Alphonse

2. You know that every data point will fall between 0 and ten.

Theonly way a ditribution can have mean 0 and be restricted between
0 and ten is if all the probability is associated with 0. That is, every data point is 0.

If you get a trial with a non zero value, then it must be possible to get nonzero values. This implies that the mean is not zero. p-value = 0.000000000000!

Not a dumb question though.

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