Question

The one sample t statistic from a sample of n = 25 observations for the one-sided test of
H0: μ = 9, Ha: μ > 9 has the value t = 1.84.
Based on this information
A. p-value = .0250.
B. p-value = .0391.
C. p-value = .2392.
D. we can not calculate the p-value.

Answer 1

You certainly can calculate the \(p\) value, but that depends on the precision of a \(t\) table you might use and the resources you have available.

For example, this table ( http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf ) tells you that the value \(t=1.84\), is greater than the critical \(t\) for a test of \(95\%\) significance. At most, you know that \(p\) is smaller than \(0.05\), but you don't know what the exact value is.

On the other hand, if you know what the explicit formula for this distribution is (a T distribution with 24 degrees of freedom), then you can use a computer to give you an approximated \(p\) value, which happens to be on the list of provided answers.

Answer 2

So if I'm only given a table, is there any formula I can use to find the p-value?

Answer 3

Not unless you can compute the following integral:
\[\large p=\int_{1.84}^\infty\frac{\Gamma\left(\dfrac{24+1}{2}\right)}{\sqrt{24\pi}~\Gamma\left(\dfrac{24}{2}\right)}\left(1+\frac{x^2}{24}\right)^{-\frac{24+1}{2}}~dx\]
I'm not familiar with any other formula for finding an approximate \(p\) value with just the given information.

Answer 4

Oh geez...well thank you for your help. I'll look into using the computer to find an exact value

Answer 5

You can use this tool here: http://www.socscistatistics.com/pvalues/tdistribution.aspx