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?

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

H_{0}: ρ_{engineers}= ρ_{humanities}

H_{1}: ρ_{engineers}≠ ρ_{humanities }where ρ_{engineers}is the population correlation between QSAT and GPA for engineering majors and ρ_{humanities}is the population correlation between QSAT and GPA for the humanities majors.

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