What will be the ‘t value’ when ‘between-groups variance’ and ‘within-groups variance’ is 200 and 50 respectively?

Correct option is B

In statistics, the 't value' can be derived from the F-ratio when comparing two groups because the square of the t-value is equal to the F-value (t^2 = F), making the correct answer 2.

Information Booster: 

• Understanding the F-ratio: The F-statistic (used in ANOVA) is calculated by dividing the variance between groups by the variance within groups.
• $$Formula: F = \frac{\text{Between-groups variance}}{\text{Within-groups variance}}$$​​
• $$​Calculation: F = \frac{200}{50} = 4$$​​
  
• The t and F Relationship: For a comparison between exactly two groups, the t-statistic and F-statistic are mathematically related. Specifically, $$F = t^2$$​.

• Calculating the t-value: Since we have the F-value, we take the square root to find $t$.

  • ​$$t = \sqrt{F}$$​​
    

  • ​$$t = \sqrt{4} = 2$$​​
    

• Conclusion: When the between-group variance is 200 and the within-group variance is 50, the resulting t-value is 2.