Question

g The p-value of the test of the null hypothesis is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. the probability the null hypothesis is true. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. the probability the null hypothesis is false.

Answer 1

Answer:

Correct option:

"assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed."

Step-by-step explanation:

The p-value is well defined as the probability,[under the null hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

A small p-value (typically p ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard H₀.

A large p-value (typically p > 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value for a one tailed test is computed as follows:

$p-value=P(TS<ts_{cal.})$  OR  $p-value=P(TS>ts_{cal.})$

The p-value for a two tailed test is computed as follows:

$p-value=2\times P(TS<ts_{cal.})$

Thus, the correct definition of p-value is given by the statement:

"The p-value of the test of the null hypothesis is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed."