Question

The size of the p-value is influenced by the type of alternative hypothesis (either one or two-tailed). True or False?

Answer 1

Let assume a testing of Hypothesis problem where T be the test statistic and t is the observed value of the test statistic.

Now p-value for Both tailed alternative hypothesis is defined as

P-value = Min { P_H0(T>t) , P_H0(T<t) }

For Right tailed alternative :

P-value = P_H0(T>t)

For Left tailed alternative:

P-value = P_H0(T<t)

Where H0 is the null hypothesis.

So it is clear that p-value depends on the type of the alternative.

Answer: True