The problem asks to identify the value of the test statistic based on the given analysis of variance (ANOVA) results.

Given:

• F (test statistic): $5.17$
• p-value: $0.011$
• Significance level: $\alpha = 0.05$

Answer:

The value of the test statistic is clearly provided in the ANOVA table under the "F" column for the Factor row, which is:

$F = 5.17$.

Thus, the correct answer is C) 5.17.

Would you like further explanation or details on ANOVA? Here are five related questions for deeper understanding:

1. What is the purpose of the F-statistic in ANOVA?
2. How do you calculate the Mean Square (MS) values in an ANOVA table?
3. What does the p-value indicate in relation to the null hypothesis in this test?
4. How does the significance level ($\alpha$) impact the interpretation of the test result?
5. Can you explain how the degrees of freedom (DF) are determined in ANOVA?

Tip: The F-statistic in ANOVA measures the ratio of variation between group means to the variation within groups. A higher F-value suggests stronger evidence against the null hypothesis.