Question

Part B:

According to a report of COVID-19 death rates in the United States from CDC as of April 6^th 2020, New York has around 21.2 per 100,000 people for the death rate, which is the state with the highest number of COVID-19 cases.

a)     Obtain a point estimate for the population proportion of Americans who have died from COVID-19 in New York state.

b)     Verify that the requirements for constructing a confidence interval about p are satisfied.

c)      Construct a 90% confidence interval for the population proportion of Americans who have died in New York since the COVID-19 pandemic.

d)     Interpret the interval.

Answer 1

a)
pcap = 0.212

b)
np = 100000 * 0.212 > 5
nq = 100000 * (1 - 0.212) > 5

c)
sample proportion, = 0.212
sample size, n = 100000
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.212 * (1 - 0.212)/100000) = 0.0013

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.212 - 1.64 * 0.0013 , 0.212 + 1.64 * 0.0013)
CI = (0.2099 , 0.2141)

d)
One can be 90% confident that the true proportion of people died in NY since the COVID 19 pandemic is between 0.2099 and 0.2141