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 believed to be better suited for doing math than girls. Recent research chalienges 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 giris, resulting in some boys with soaring math skills. The accompanying data file shows the math scores for 22 boys and 22 girls. Click here for the Excel Data File a. Construct 95% confidence intervals for the mean scores of boys and the mean scores of girls. Note: Round your final answers to 2 decimal places. b. Explain why the widths of the two intervals are different: The sample standard errors of the scores of boys and girls are different. The sample means of the scores of boys and girls are different.begin{tabular}{|r|r|} hline Boys & Girls hline 77 & 78 hline 88 & 76 hline 96 & 84 hline 79 & 81 hline 68 & 99 hline 89 & 86 hline 79 & 96 hline 96 & 71 hline 100 & 85 hline 66 & 76 hline 99 & 81 hline 78 & 95 hline 79 & 72 hline 60 & 67 hline 100 & 83 hline 43 & 84 hline 93 & 71 hline 89 & 61 hline 87 & 60 hline 67 & 98 hline 92 & 91 hline 62 & 77 hline end{tabular}.

1. 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 believed to be better suited for doing
math than girls. Recent research chalienges 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 giris,
resulting in some boys with soaring math skills. The accompanying data file shows the math
scores for 22 boys and 22 girls. Click here for the Excel Data File a. Construct 95% confidence
intervals for the mean scores of boys and the mean scores of girls. Note: Round your final
answers to 2 decimal places. b. Explain why the widths of the two intervals are different: The
sample standard errors of the scores of boys and girls are different. The sample means of the
scores of boys and girls are different.begin{tabular}{|r|r|} hline Boys & Girls hline 77 & 78 hline 88
& 76 hline 96 & 84 hline 79 & 81 hline 68 & 99 hline 89 & 86 hline 79 & 96 hline 96 & 71 hline 100
& 85 hline 66 & 76 hline 99 & 81 hline 78 & 95 hline 79 & 72 hline 60 & 67 hline 100 & 83 hline 43
& 84 hline 93 & 71 hline 89 & 61 hline 87 & 60 hline 67 & 98 hline 92 & 91 hline 62 & 77 hline
end{tabular}