Question

The ratio of two independent chi-square variables is _______.

• A. Normal
• B. t-statistic
• C. Chi-square statistic
• D. F-statistic

Hint:

The F-statistic is used in statistical tests, particularly in ANOVA, where it is the ratio of two chi-square variables, each divided by its respective degrees of freedom.

Answer 1

The Correct Option is D

Step 1: Understanding the F-statistic.
The ratio of two independent chi-square variables, each divided by its respective degrees of freedom, follows an F-distribution. The F-statistic is used in ANOVA and hypothesis testing.
Step 2: Analyzing the options.

• (A) Normal: Incorrect. The ratio of chi-square variables does not follow a normal distribution.
• (B) t-statistic: Incorrect. The t-statistic is used for comparing means, not for the ratio of chi-square variables.
• (C) Chi-square statistic: Incorrect. A chi-square statistic is used for variance and independence tests, not for the ratio of chi-square variables.
• (D) F-statistic: Correct. The ratio of two independent chi-square variables follows an F-distribution.

Step 3: Conclusion.
The correct answer is (D) F-statistic, as the ratio of two independent chi-square variables follows an F-distribution. Final Answer:} F-statistic.