# Solved – Can someone show me how to use the t-table and find p? Hypothesis testing

hypothesis testing

Can someone show me how to use the table? I know that T is 0.745 but how do I find P and use the table.

Notice two things in the table.

• For a given value of $$\nu$$, an increase of the $$t$$-value corresponds to a decrease of the $$\alpha$$-level (or p-value). That means high $$t$$-values are rarer when the null-hypothesis is true (if you observe a high $$t$$-value then this is 'special').

• For a given $$\alpha$$-level the t-values to obtain this level are lower when $$\nu$$ increases.

(sidenote: the table is for positive t-values, but the same can be done for negative t-values)

Intuitively: you find the t-value by dividing the mean by the estimate of the variance. This estimate of the variance is a variable whose variance depends on the size of the sample. Every time you perform an experiment it will be different, and the smaller the sample the larger this difference.

So a smaller sample size will cause the $$t$$-score to differ to a larger extent from experiment to experiment. When your sample is smaller, then the variance in the $$t$$-score will be larger and therefore larger $$t$$-score values will be less 'special'.

You should look at the row for $$\nu = 29$$

                  alpha

0.40    0.25   0.10   0.05

nu    29     0.256   0.683  1.311  1.6999


You are not gonna find the value exactly but, what kind of $$\alpha$$ or $$p$$ does the t-value $$0.745$$ correspond to? Between which two $$p$$ values should it be?