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.

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Best Answer

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?

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