A researcher studying hate crimes notices that more hate crimes tend to happen in states with larger populations. Table 13.16 shows a cross-tabulation of states’ population and prevalence of hate crimes.

a. What is the relationship between population and prevalence of hate crimes, as shown in Table 13.16?

b. Tables 13.17 and 13.18 show two hypothetical cross-tabulations of state population by hate crime prevalence, controlling for whether states have hate crime laws that cover sexual orientation and gender identity. Answer the following question for both tables: is there a relationship between state population and prevalence of hate crimes once the protection of sexual orientation and gender identity is held constant?

c. Answer this question for Table 13.17 and 13.18: Is the relationship between state population and hate crime prevalence spurious? Explain your answer.

d. Real data suggest that hate crime laws may not deter hate crimes. Is this finding contradicted by Table 13.17? By Table 13.18?