Math Problem Statement
Solution
The best statement that defines statistical significance among the options provided is:
"There is less than 5% probability of obtaining the observed results if the null hypothesis is true."
Explanation:
Statistical significance is generally defined by the probability that the observed result would occur if the null hypothesis were true. A result is considered statistically significant if this probability (the p-value) is lower than a predetermined threshold, often 5% (or 0.05). This implies that there's less than a 5% chance that the observed data would occur under the assumption that there is no effect or difference (the null hypothesis).
Would you like further details on this topic, or do you have any questions?
Here are some related questions to expand your understanding:
- What is the null hypothesis in statistical testing?
- How is the p-value calculated, and what does it represent?
- What is the difference between statistical significance and practical significance?
- Why is the 5% level often chosen as the threshold for statistical significance?
- How can sample size affect statistical significance?
Tip: Remember that statistical significance does not imply practical importance; it only indicates that the result is unlikely due to random chance.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Hypothesis Testing
Statistical Significance
Formulas
P-value calculation
Theorems
Central Limit Theorem
Null Hypothesis Testing
Suitable Grade Level
Grades 11-12, College Level
Related Recommendation
Understanding Statistical Significance in Hypothesis Testing
Interpreting P-Value in Hypothesis Testing for Statistical Significance
Understanding Hypothesis Testing with a 55% Significance Level
Hypothesis Testing Decision Rule: P-value vs Significance Level
Determine Whether to Reject the Null Hypothesis Using p-value and Significance Level