Tests of Differences between Independent Pearson Correlations (1 of 5)

A researcher was interested in whether the relationship between the quantitative portion of the SAT (QSAT) and grades in the first year of college (GPA) is different for engineering majors than it is for humanities majors. One hundred engineering majors and 100 humanities majors were sampled and each student's QSAT and GPA were recorded. The Pearson's correlation between these two measures was 0.61 for the engineering majors and 0.35 for the humanities majors. Is this difference in correlations significant?

  1. The first step is to specify the null hypothesis and an alternative hypothesis. The null hypothesis and alternative hypotheses for this problem are:

    H0: ρengineers = ρhumanities
    H1: ρengineers ≠ ρhumanities

    where ρengineers is the population correlation between QSAT and GPA for engineering majors and ρhumanities is the population correlation between QSAT and GPA for the humanities majors.

  2. The second step is to choose a significance level. Assume the 0.05 level is chosen.