Question

How do you calculate the p-value in a hypothesis test?

Answer 1

p-value is the probability of getting as or more extreme sample, as observed, if null hypothesis was true. We test this in the direction of alternative hypothesis.

For example: if we test `H_0: \mu = 10` vs `H_a: \mu > 10`, and we get test statistic `z = 1.96`, then p-value is the probability of getting this test statistic in the direction of alternative hypothesis, i.e, p-value = `P(Z>1.96) = 0.025`

(probability is obtained from test-statistics distribution, here it came from z-table).