Question

It is estimated that at the peak of the COVID-19 pandemic, 1.5 out of 87 people in New York will be infected with the virus. Construct a 99% confidence interval for the proportion of infected people in New York.

Answer 1

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 1.5

n = 87

P = x/n = 1.5/87 = 0.017241

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.017241 ± 2.5758* sqrt(0.017241*(1 –0.017241)/87)

Confidence Interval = 0.017241 ± 2.5758* 0.0140

Confidence Interval = 0.017241 ± 0.0359

Lower limit = 0.017241 - 0.0359 = -0.0187

Upper limit = 0.017241 + 0.0359 = 0.0532

Confidence interval = (-0.0187, 0.0532)