How to find a p-value from t-stat When you have a t-statistic and a standard error, how can you find a p-value?
Specifically, I am given this question a t-statistic of 1.363, and a standard error of 0.733.
And the following table:

The answer is a pvalue of  0.173. How do I find the pvalue?
 A: There are a few issues here.

*

*What you're showing here is a table of Z-statistics (for the Normal distribution), not t-statistics (for the Student t distribution). If you really want to compute p-values for the $t$ distribution you'll need (1) to be told what the 'df' or degrees-of-freedom parameter is; (2) another set of tables that give values for the $t$ statistic.

*the standard error is irrelevant (maybe this is included by your instructor to see if you know you don't really need it?), the Z or t statistic already incorporates it ($Z = t = \mu/\sigma$).


*

*you can look up how to read a p-value from a $Z$ table here, except that the Z-table illustrated there is different from the one you're showing here: your table shows the area under the curve between $Z=0$ and the value indicated by the row/column combination, whereas the table in the link shows the area under the curve between $-\infty$ and $Z$ (i.e., your values are 0.5 less than the values in the linked table, because $P(-\infty< Z <0)$ is 0.5)*.

*

*the value in the "1.3" row and the "0.06" column is 0.413.

*the upper tail probability (the probability that a draw from the standard Normal is $\geq Z$) is 0.5-0.413 (why subtract from 0.5? The probability that $Z>0$ is 0.5; the probability that $0<Z<1.36$ is 0.413; therefore the probability that $Z>1.36$ is 0.5-0.413)

*the two-tailed p-value is $2 \times (0.5 - 0.413) = 0.174$ (as close as you can get to the specified answer with this table).



It's kind of weird that someone is asking you to do this; given the availability of statistics packages, it's a little bit like learning to light a fire without matches (without the fun and survival value).
In R, you would compute 2*pnorm(1.363, lower.tail = FALSE)

* Please forgive abuse of notation ...
