And did these students experience an improvement in schoolwork achievement? If we don’t know this, (A) has no impact.

Pre-program levels of achievement are irrelevant, since the author never compared the absolute achievement levels of the students who completed the program to those of the students who didn’t. We still know the program-completers increased their achievement after the program.

This suggests a potential alternate hypothesis for the increase in achievement levels observed in the study. If many of the children wanted to join a team that required a high grade average, that could have motivated these students to do better on their schoolwork.

The author never assumed that chess is the only activity that can improve student achievement. And, since we have no reason to think that the students who completed the chess program attended the sessions described in (D), this answer has no impact.

We don’t know whether the students described in (E) experienced an increase in achievement levels. In addition, varyling levels of chess talent don’t necessarily impact the level of reasoning power or spatial intuition exercised during chess.