Part 6: Inference

Goals

• Calculate and analyze confidence intervals to estimate population proportions
• Perform hypothesis tests and analyze p-values

Task 6.1 Confidence intervals

Open the 2016 data spreadsheet for The Counted

1. Determine the sample proportions of cases of the following race/ethnicities
   1. White
   2. Black
   3. Hispanic/Latino
2. Explain how these data meet the conditions for estimating the corresponding population proportions using confidence intervals.
   1. Independent data–does one case’s status affect another case’s status? 
   2. Sample size(s) large enough—do we have 10 or more “yes” and “no” for the category we’re curious about?
3. Use technology to construct a 95% confidence interval to estimate the proportion of people killed by police who are 

1. White
2. Black
3. Hispanic/Latino

4. Communicate the meanings of these confidence intervals in language that someone who hasn’t taken a statistics class would understand. Remember to communicate
   1. what’s being estimated (population parameter)
   2. the estimated range(s) (interval)
   3. how confident you are about the estimate(s) (confidence level)
5. Demographically, White people represented 72.4% of the US population (in 2014). How does this proportion compare with your estimate of the proportion of people killed by police who are White?
6. Based on The Counted data, construct and complete the confidence interval table below to estimate the proportion of people killed by police who are Asian.

7. Considering the table above, answer the following questions:

1. As the confidence level decreases, what happens to the width of the interval? Why?
2. As the confidence level increases, what happens to the margin of error? Why?
3. If the confidence level were 98%, would the confidence interval estimate be more or less precise than for 95% confidence? Why?

Task 6.2 Hypothesis testing

8. Perform a hypothesis test to examine the claim that the proportion of people killed by police who are Hispanic/Latino is different from 16.4% (the 2014 demographic percentage for Hispanic/Latino Americans in the US population).
   1. Clearly state the null and alternative hypotheses to test, both as sentences and using symbols.
   2. Are the conditions (independent data and large enough sample size) met?
   3. Use technology to calculate the test statistic and the P-value.
   4. Make a sketch showing the distribution and the P-value.
   5. Using significance level 0.05, do you reject the null hypothesis or not?
   6. Communicate the conclusion of your hypothesis test in context.
9. Now perform a hypothesis test to examine the claim that the proportion of people killed by police in the US who are Black is different from 12.6% (the 2014 demographic percentage for Black Americans in the US population).
   1. Clearly state the null and alternative hypotheses to test, both as sentences and using symbols.
   2. Are the conditions (independent data and large enough sample size) met?
   3. Use technology to calculate the test statistic and the P-value.
   4. Make a sketch showing the distribution and the P-value.
   5. Using significance level 0.05, do you reject the null hypothesis or not?
   6. Communicate the conclusion of your hypothesis test in context.

Task 6.3 Analysis

10. Based on your confidence intervals and hypothesis tests, 
    1. Does The Counted 2016 data indicate that there is correlation between race/ethnicity and being killed by police?
    2. How would you explain these results to a friend who hasn’t taken a statistics class?

Further resources

If you’re curious about policy ideas that could decrease the number of police killings, there are many organizations committed to the work. One national organization is Campaign Zero. One local organization is Don’t Shoot Portland.