Statement (I): t-test and F-test are based on the identical assumptions.

Statement (II): t-test is used for comparison between two groups whereas F-test is used for comparison between more than two groups.

In the context of the above two statements, which one of the following codes is correct?

Correct option is A

Statement (I): t-test and F-test are based on identical assumptions.
· Reassessing Assumptions of t-test and F-test:
· Both t-test and F-test share some common assumptions, such as:
1. Normality: The data should be approximately normally distributed in both tests.
2. Independence: Observations within each group must be independent.
3. Equal Variance (Homogeneity of Variance):
· In a t-test for independent samples, equal variance is assumed under a specific version (pooled variance t-test).
· F-test assumes equal variance across groups, which is necessary in ANOVA.
· Since both tests rely on similar key assumptions (normality, independence, and homogeneity of variance), Statement (I) is correct.
Statement (II): t-test is used for comparison between two groups, whereas F-test is used for comparison between more than two groups.
· This is true:
· A t-test is specifically designed to compare the means of two groups (e.g., independent samples or paired samples).
· The F-test, particularly in ANOVA, is used to compare the means of three or more groups, making it appropriate for analyzing variability across multiple datasets.
· Conclusion: Statement (II) is correct.