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. 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 the data on math scores of boys and girls is shown below; the complete data set, labeled Math_Scores, can be found on the text website.
Boys Girls
74........ 83
89........ 76
: ......... :
66........ 74
a. Use Excel to construct 95% confidence intervals for the mean scores of boys and the mean scores of girls. Explain your assumptions.
b. Explain why the widths of the two intervals are different.