Decide whether to reject the null hypothesis. Choose the correct answer below.

A.

RejectReject 

the null hypothesis because the​ P-value is 

less than or equal toless than or equal to 

the significance​ level, 

alphaα.

B.

Fail to rejectFail to reject 

the null hypothesis because the​ P-value is 

less than or equal toless than or equal to 

the significance​ level, 

alphaα.

C.

RejectReject 

the null hypothesis because the​ P-value is 

greater thangreater than 

the significance​ level, 

alphaα. 

D.

Fail to rejectFail to reject 

the null hypothesis because the​ P-value is 

greater thangreater than 

the significance​ level, 

alphaα.

The correct answer is:

**D. Fail to reject the null hypothesis because the​ P-value is greater than the significance level, alpha (α).**

Explanation:
- If the **P-value** is **greater than** the significance level (α), it means there is not enough evidence to reject the null hypothesis. Therefore, you "fail to reject" the null hypothesis.
- If the **P-value** is **less than or equal to** the significance level (α), you would reject the null hypothesis.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is a P-value in hypothesis testing?
2. How do you choose the significance level (α) for a test?
3. What are Type I and Type II errors in hypothesis testing?
4. How does the sample size affect the P-value in hypothesis testing?
5. What is the relationship between confidence intervals and hypothesis testing?

**Tip:** Always check the significance level (α) before making a conclusion about the null hypothesis, as it sets the threshold for decision-making.

Decide whether to reject the null hypothesis. Choose the correct answer below.
A. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha (α).
B. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha (α).
C. Reject the null hypothesis because the P-value is greater than the significance level, alpha (α).
D. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha (α).

Learn how to decide whether to reject or fail to reject the null hypothesis using P-value and the significance level (alpha). Understand key concepts in hypothesis testing, including how to interpret the P-value in relation to alpha. This solution is ideal for college-level statistics students.

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