• Complete a two-sample [latex]t[/latex]-test for independent population means from hypotheses to conclusions

Hate Crime in California

A hate crime is defined as a criminal offense that is motivated, in whole or in part, by the offender’s bias(es) against a person based on race, ethnicity, ancestry, religion, sexual orientation, disability, gender, and gender identity. ^[1] In the year 2020, [latex]62\%[/latex] of victims were targeted because of the offenders’ bias toward race/ethnicity/ancestry, which continues to be the largest bias motivation category. Participating agencies reported [latex]5,227[/latex] race/ethnicity/ancestry-based incidents in 2020, a [latex]32\%[/latex] increase from 2019. Anti-Black or African American hate crimes continue to be the largest bias incident victim category, with [latex]2,871[/latex] incidents in 2020, a [latex]49\%[/latex] increase since 2019. Additionally, there were [latex]279[/latex] anti-Asian incidents reported in 2020, a [latex]77\%[/latex] increase since 2019. The other largest categories of hate crimes include anti-Hispanic or Latino incidents, with [latex]517[/latex], and anti-White incidents, with [latex]869[/latex] in total.

Suppose we wanted to study the increase in hate crime from 2019 to 2020, specifically in the state of California.

Previously, you have conducted a one-sample [latex]t[/latex]-test (a hypothesis test about a population mean). We can apply the same steps to analyze and test a hypothesis about the difference in means for two independent populations. A hypothesis test for comparing two population means is often referred to as a two-sample [latex]t[/latex]-test.

Note: Previously, we have verified that the assumptions for a two-sample [latex]t[/latex]-test were met for the Hate Crime data set for the state of California. We know that the two samples were independent, representative of the populations of interest, and large.

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