Question

With Everything else held fixed, the P-value of a one-sided test is always half that of the corresponding two-sided test.

Why this statement is false? Please give an explanation, thank you.

Answer 1

Solution:-

False, the P-value of a one-sided test is not always half that of the corresponding two-sided test.

In few cases the p-value of one-sided test is half that of the corresponding two-sided test, whereas the case is always same.

Case I

One tailed test.

Null hypothesis: u < X
Alternative hypothesis: u > X

Let z = 2.2

p-value for right tailed test is P(z > 2.2) = 0.014

Two tailed test

Null hypothesis: u = X
Alternative hypothesis: u X

Let z = 2.2

p-value for right tailed test is P(-2.2 > z > 2.2) = 0.028

Case II

One tailed test.

Null hypothesis: u > X
Alternative hypothesis: u < X

Let z = 2.2

p-value for left tailed test is P(z < 2.2) = 0.986

Two tailed test

Null hypothesis: u = X
Alternative hypothesis: u X

Let z = 2.2

p-value for right tailed test is P(-2.2 > z > 2.2) = 0.028