The p-value Question 4Select one:a.can be any value, negative or positiveb.must be a number between zero and 1c.can be any valued.can be any positive value

Break Down the Problem

1. Identify the Concept: Understanding what a p-value is in statistical hypothesis testing.
2. Determine Valid Options: Assess which of the provided options correctly describes the characteristics of a p-value.

Relevant Concepts

• Definition of p-value: The p-value is a measure of the evidence against a null hypothesis. It indicates the probability of obtaining results as extreme as the observed results, given that the null hypothesis is true.

Analysis and Detail

1. Option a: "can be any value, negative or positive" - Incorrect. P-values cannot be negative because they represent probabilities.
2. Option b: "must be a number between zero and 1" - Correct. A p-value ranges from 0 to 1, where a smaller p-value indicates stronger evidence against the null hypothesis.
3. Option c: "can be any value" - Incorrect for the same reason as option a, as probabilities cannot exceed 1.
4. Option d: "can be any positive value" - Misleading. While p-values are positive, they are specifically constrained between 0 and 1.

Verify and Summarize

The correct understanding of p-values confirms that they serve a specific role in hypothesis testing and must lie within the range of 0 to 1. Therefore, option b is the only valid choice.

Final Answer

b. must be a number between zero and 1.