Question

According to a report of COVID-19 death rates in the United States from CDC as of April 6th 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

Answer:

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

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