# Question: Let x denote the test statistic for a hypothesis test

Let x denote the test statistic for a hypothesis test and x0 its observed value. Then the P-value of the hypothesis test equals

a. P(x ≥ x0) for a right-tailed test,

b. P(x ≤ x0) for a left-tailed test,

c. 2 ∙ min{P(x ≤ x0), P(x ≥ x0)} for a two-tailed test,

Where the probabilities are computed under the assumption that the null hypothesis is true. Suppose that you are considering a one-mean z-test. Verify that the probability expressions in parts (a)-(c) are equivalent to those obtained in Exercise 9.61.

a. P(x ≥ x0) for a right-tailed test,

b. P(x ≤ x0) for a left-tailed test,

c. 2 ∙ min{P(x ≤ x0), P(x ≥ x0)} for a two-tailed test,

Where the probabilities are computed under the assumption that the null hypothesis is true. Suppose that you are considering a one-mean z-test. Verify that the probability expressions in parts (a)-(c) are equivalent to those obtained in Exercise 9.61.

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