Two machines produce metal rods. You take independent random samples of their lengths (shown below) as part of a hypothesis test. Calculate the F statistic for this test.
Sample A: $s^2=2.1,n=10$
Sample B: $s^2=4.2,n=12$

• A. 4
• B. 2
• C. 2.4
• D. 4.8

Answer: (B)

Verified step by step guidance

1. Understand that the F-distribution is used primarily to compare two variances and is often applied in the context of ANOVA or hypothesis testing about variances.
2. Identify the degrees of freedom for the numerator (df1) and the denominator (df2), which correspond to the sample sizes or groups involved in the problem.
3. Determine the critical value or the p-value from the F-distribution table or software using the given degrees of freedom and the significance level (usually denoted as \( \alpha \)).
4. Set up the hypothesis test: the null hypothesis \( H_0 \) typically states that the variances are equal, and the alternative hypothesis \( H_a \) states that they are not equal (or one variance is greater than the other, depending on the test).
5. Compare the calculated F-statistic from your data to the critical value to decide whether to reject or fail to reject the null hypothesis.