Question: For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing that gender differences in math performance have more to do with culture than innate aptitude. In the U.S., for example, girls perform just as well on standardized math tests as boys. Others argue, however, that while the average may be the same, there is more variability in math ability for boys than girls, resulting in some boys with soaring math skills. A portion of representative data on math scores of boys and girls is shown below; the complete data, labeled Math Scores, are available on the text website.
In a report, use the above information to:
1. Construct and interpret 95% confidence intervals for the ratio of the variance of math scores for boys and for girls. Discuss the assumptions made for the analysis.
2. Determine at the 5% significance level if boys have more variability in math scores than girls.