For given problem, suppose that the appropriate sample means are 6.4, 2.5, and 4.9 (as scores for participation by European American, African-American, and Other models in commercials). Find where differences, if any, exist among the three population means. Use α = 0.05.

Problem
A study was undertaken to assess how both majority and minority groups perceive the degree of participation of African-American models in television commercials. The authors designated the three groups in this study as European Americans, African Americans, and Other.

The purpose of this research was to determine if there were any statistically significant differences in the average perceptions within these three groups of the extent of the role played by African-American models in commercials the subjects viewed.

The results of the ANOVA carried out were summarized as F(2, 101) = 3.61. Analyze this result and state a conclusion about this study.