Exercise 6-27 Algo 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 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. 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. Mean scores of boys Mean scores of girls ces Confidence intervals to to 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. Boys Girls 72 86 90 80 94 84 84 84 63 99 90 92 87 96 96 72 100 86 67 82 99 73 72 97 85 75 59 66 100 80 44 85 83 78 93 61 86 66 66 98 95 89 71 71