# Calculate the two-sided p-value 2P(t>3.21) where t is a t statistic

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### 1 Answer

t represents a t-statistic. This will usually be of the form (observation-expected value under null)/estimated sd.

With the t-distribution the number of *degrees of freedom* is important when calculating the p-value. The number of degrees of freedom is equal to n minus the number of free parameters in the statistic (ie the number being estimated). This will be *n-1* for a one-sample test, since we are estimating just one mean.

Suppose the sample size is n=20 for example. For a one-sample test, the number of degrees of freedom is then 19. Then, using lookup tables,

P(t>3.21|df = 19) = 0.00230

Therefore, 2P(t>3.21|df = 19) = 0.00461

Since we are considering the two tails of the t-distribution, this is a two-sided test. The null (that the true mean is equal to some pre-specified value) is rejected at the 0.005 x 100 = 1/2 % level since the two-sided p-value is less than 0.005.