or 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 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.   Explain why the widths of the two intervals are different. multiple choice 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   71 88   85 76   96 92   85 82   67 99   85 88   84 96   96 64   100 87   57 76   99 79   77 89   89 71   53 67   100 87   44 87   93 78   90 71   90 66   64 98   90 86   70 72

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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

  1. 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.

     
  2. Explain why the widths of the two intervals are different.

    multiple choice

    • 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  
71 88  
85 76  
96 92  
85 82  
67 99  
85 88  
84 96  
96 64  
100 87  
57 76  
99 79  
77 89  
89 71  
53 67  
100 87  
44 87  
93 78  
90 71  
90 66  
64 98  
90 86  
70 72  
     
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