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:
- What is a P-value in hypothesis testing?
- How do you choose the significance level (α) for a test?
- What are Type I and Type II errors in hypothesis testing?
- How does the sample size affect the P-value in hypothesis testing?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Hypothesis Testing: Rejecting the Null Hypothesis H0 at Alpha = 0.05
Determine Hypothesis Test Results Based on Significance Level and P-Value
Interpreting P-Value in Hypothesis Testing for Statistical Significance
Hypothesis Test Decision Based on p-value: Accept or Reject H0
How to Interpret a P-value of 0.028 in Hypothesis Testing