Question

On April 7th, 2020, a New York Times article reported that a disproportionate number

of African Americans are dying from complications of the virus. In Illinois 43% of people who

have died from the disease and 28% of those who have tested positive are African-American

even though they only make up 15% of the state’s population. Suppose we looked at another

ethnic group in Illinois and called them Sample 2 and the African-Americans were Sample 1.

a. Suppose we looked at their rates of testing positive for the two groups. The following two-

sample proportion confidence interval was given: (-0.03, 0.12), can we conclude that the two

groups have statistically different positive testing rates? Briefly explain.

b. Now we wanted to look at the percent who are dying from the disease. The following two-

sample proportion confidence interval was given: (0.05, 0.17), can we conclude that the two

groups have statistically different rates of dying from the disease? Briefly explain.

c. If we looked at another ethnic group in Illinois, what would we need to see in our confidence

intervals to “show” that the percent when comparing it to the African-Americans is

statistically different?

Answer 1

(a)

Since the two-sample proportion confidence interval (-0.03, 0.12) of the difference in positive testing rates of the 2 groups includes 0, (i.e., the confidence interval contains both positive, negative and 0 values), we cannot conclude that the two groups have statistically different positive testing rates.

(b)

Since the two-sample proportion confidence interval (0.05, 0.17) of the difference in positive testing rates of the 2 groups contains only positive values, we can conclude that the two groups have statistically different rates of dying from the disease.

(c)

To “show” that the percent when comparing it to the African-Americans is statistically different, we would need to see in our confidence intervals: the confidence interval for the difference in proportions should not contain 0, i.e., all the values in the confidence interval should be either all positive or all the values in the confidence interval should be all negative.