Math Problem Statement

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.

Solution

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.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
P-value
Significance Level (α)

Formulas

If P-value ≤ α, reject the null hypothesis
If P-value > α, fail to reject the null hypothesis

Theorems

Hypothesis Testing Theorem

Suitable Grade Level

College-Level Statistics