Math Problem Statement
Question 27 (1 point)
- Represents a parametric statistical test for significance:
Question 27 options:
Hypothesis test for β = 0
ANOVA
both choices "A" and "B" are correct
neither choices "A" nor "B" are correct
Solution
The correct answer is:
both choices "A" and "B" are correct.
Explanation:
-
Hypothesis test for β = 0: This is a parametric test often used in linear regression. It assesses whether the slope of the regression line (β) is significantly different from zero, using a t-test or F-test.
-
ANOVA (Analysis of Variance): This is another parametric test used to compare means among multiple groups to determine if there is a statistically significant difference between them. ANOVA assumes normality of the data and homogeneity of variance.
Since both tests are parametric and test for statistical significance, the correct answer is both A and B are correct.
Would you like further explanation or examples on parametric tests?
Related Questions:
- What are the key assumptions underlying parametric tests?
- How does a t-test differ from ANOVA in practical applications?
- What is the role of the F-distribution in hypothesis testing?
- Why are parametric tests preferred in certain scenarios over non-parametric tests?
- How do you interpret p-values in hypothesis tests?
Tip:
Always verify the assumptions of normality and variance homogeneity before applying parametric tests to ensure the validity of your results.
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Math Problem Analysis
Mathematical Concepts
Parametric Statistical Tests
Linear Regression
Analysis of Variance (ANOVA)
Formulas
t-test for hypothesis testing: t = (β - 0) / SE(β)
F-test in ANOVA: F = (MS_between) / (MS_within)
Theorems
Central Limit Theorem
F-distribution in ANOVA
Suitable Grade Level
Undergraduate (Statistics or Applied Mathematics)