The following table shows scores on the first quiz (maximum score 10 points) for eighth-grade students in an introductory level French course. The instructor grouped the students in the course as follows:
Group 1: Never studied foreign language before but have good English skills
Group 2: Never studied foreign language before and have poor English skills
Group 3: Studied at least one other foreign language

a. Defining notation and using results obtained with software, also shown in the table, report the five steps of the ANOVA test.
b. The sample means are quite different, but the P-value is not small. Name one important reason for this.
c. Was this an experimental study, or an observational study? Explain how a lurking variable could be responsible for Group 3 having a larger mean than the others. (Thus, even if the P-value were small, it is inappropriate to assume that having studied at least one foreign language causes one to perform better on this quiz.)

French scores on the quiz Group 1 Group 2 Group 3 10 3.0 2.828 8.0 2.646 Mean 6.0 Std. Dev. 2.000 Source Group Error Total DF MS 30.00 15.00 30.00 6.00 60.00 2.50 0.177