male students

19

5. Data Analysis

The data we analyze are from the scores of Calculus exams (midterm and final) that were applied to a class of students from Department of Chemistry, National Taiwan Normal University. In this class, there are 32 male students and 8 female students. We are interested in whether the correlations between the two scores (midterm and final) are different among male and female students.

The data are shown in the following.

male students

midterm 68 74 58 53 68 72 71 61 45 76 57 final 64 75 62 55 79 24 74 59 26 36 38

midterm 44 60 71 79 58 69 80 85 84 82 49 final 27 31 43 75 56 49 42 73 64 44 66

midterm 73 80 57 58 40 47 83 59 9 50 final 78 76 62 56 14 48 67 38 0 28

female students

midterm 60 61 64 64 68 76 55 37

final 51 39 57 79 66 55 64 19

20

Let

r

=Pearson correlation coefficient for male students’s midterm and final scores.

r

=Pearson correlation coefficient for female students’s midterm and final scores.

CI(I)= Confidence Interval I.

CI(II)= Confidence Interval II.

CI(III)= Confidence Interval III.

LI= length of CI(I).

LII= length of CI(II).

LIII= length of CI(III).

The analysis results are displayed in Table 7.

Table 7

r

r

r

− r

0.637717 0.664064 -0.026347

CI(I) CI(II) CI(III)

[ −0.72082, 0.66813] [−0.41220, 0.46489] [−0.38934, 0.35886]

LI LII LIII

1.38895 0.87710 0.74820

LII−LIII LI−LIII LI−LII

0.12889 0.64075 0.51185

We can see from Table 7 that the confidence interval III provides the most precise result among the three intervals. Based on this confidence interval, we are 95% confident to say that

−0.38934 ≤ ρ

− ρ

≤ 0.35886.

It seems that the difference of the correlation coefficients among male and female students

are not statistically significant.