Question

Under the assumption of analysis of variance, the parent population should be-

• A. Normally Distributed
• B. Binomial Distribution
• C. Poisson Distribution
• D. Beta Distribution

Hint:

ANOVA requires: Normality, independence, and equal variance (homoscedasticity).

Answer 1

The Correct Option is A

Step 1: Understanding ANOVA.
Analysis of Variance (ANOVA) is a statistical tool used to compare the means of multiple groups.
It is based on the partitioning of total variance into variance between groups and variance within groups.
Step 2: Distribution assumption.
For the F-test used in ANOVA to be valid, the parent population (from which samples are drawn) must be normally distributed.
This ensures the sampling distribution of the test statistic follows the F-distribution.
Step 3: Analysis of options.
- (1) Normally distributed: Correct, this is the required assumption.
- (2) Binomial: Deals with success-failure trials, not suited for ANOVA assumption.
- (3) Poisson: For rare events, not applicable here.
- (4) Beta: Continuous distribution for bounded variables, not an assumption in ANOVA.
Step 4: Conclusion.
Thus, for ANOVA, the parent population must be normally distributed.