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

Hate Crimes

Hate crime is a crime motivated by bias against race, color, religion, national origin, sexual orientation, gender, gender identity, or disability.^[1]

The tragic toll of the COVID-19 pandemic has been compounded by a surge in violence against communities of color, including Asian American and Black communities in the United States.^[2] In August 2021, the Federal Bureau of Investigation (FBI) released Hate Crime Statistics 2020, an annual compilation of bias-motivated incidents in the United States. Though the number of reporting agencies decreased by [latex]452[/latex] since 2019, the overall number of reported incidents increased by [latex]949[/latex], contributing to a total of [latex]8,263[/latex] hate crime incidents against [latex]11,126[/latex] victims in 2020. While annual law enforcement agency participation may fluctuate, the statistics indicate that hate crimes remain a concern for communities across the country.^[3]

To analyze the claim above, let’s analyze the hate crime data from the state of California.^[4] The data set below is the rate of hate crimes reported per [latex]100,000[/latex] people for 47 of 58 counties in the state of California for the year 2019 and the year 2020.

Note: Consider the hate crime rates for each county in 2019 and 2020 as two separate datasets. Each dataset represents a distinct sample that reflects statewide hate crime rates for that particular year. The goal is to compare the overall state trends between the two years without making direct comparisons for the same counties. This means you should not pair or link the data for a county from one year with its data from another year. Instead, you’ll compare two groups: one group consisting of all counties’ rates in 2019 and another group consisting of all counties’ rates in 2020.

When we are interested in estimating a difference in population means, we usually start with data from a sample from each of the populations of interest.
There are two different strategies for selecting the two samples. One strategy is to select a sample from one population and then independently select a sample from the second population. Using this strategy results in two samples where the individuals selected for the first sample do not influence the individuals selected for the second sample. This would be the case if you take a random sample from each population.

Samples selected in this way are said to be independent samples.

Step 1: Select the “Several Groups” tab in the statistical tool
Step 2: Under “Enter Data”, select “Your Own”
Step 3: Edit “Group Labels”. Change Group 1 to “Year 2019” and Group 2 to “Year 2020”
Step 4: Copy the data set accordingly.

Year 2019

2.6
6.3
2.3
4.7
3
3.6
0.5
1.6
3.5
7.4
0.6
0.8
0.7
4.7
3.3
4.1
5
2.3
0.4
1.6
1.4
1
2.3
1.5
1.5
1
1.6
1.1
3
7.4
0.7
4.6
2.2
0.2
2.6
3.7
0.6
1.6
2.2
1.3
1
3.1
0.2
1.8
0.8
2.3
1.3

Year 2020

3.1
7.5
1.4
4.6
2.3
3.6
2.6
1.7
3.5
2.2
1.1
1.2
0.7
4.7
3.3
5.3
8.6
1.2
1.1
2.1
1.4
1
2.6
2.5
1.6
1.4
1.6
2
3.7
6.2
1.3
4.6
2.5
0.9
6.3
4.8
3.9
3.6
5.3
3.1
4.2
6.2
0.4
1.8
1.8
8.2
2.5

[Trouble viewing? Click to open in a new tab.]

---