Free Lunch. In the publication “What Makes a High School Great?” (Newsweek, May 8, 2006, pp. 50–60), B. Kantrowitz and P. Wingert looked for America’s best high schools. One relevant variable is the percentage of the student body that is eligible for free and reduced lunches, an indicator of socioeconomic status. A percentage of 40% or more generally indicates a high concentration of children in poverty. The following table provides the percentages for independent simple random samples of high schools from the four U.S. regions.

Northeast South Midwest West 15.3 41.8 12.4 26.0 3.3 18.4 7.2 45.6 13.2 11.0 1.0 3.3 10.0 18.0 2.0 45.0 5.9 30.7 58.0 10.0 16.0 50.0 2.0 26.8 1.0 7.4 2.8 10.0 40.5 8.0 13.0 11.0 6.0 At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean percent eligibility for free and reduced lunches among the four regions of the United States?