Question

Assume a city has a population of 120,000 individuals. COVID-19 has been found in this city and is estimated to infect 5%, or 6,000, of its citizens in the next month. Local hospitals want to ensure they have enough beds for those cases that require hospitalization.

To make sure they accommodate everyone in a worst-case scenario, they will use the maximum number (the upper bound) of cases requiring hospitalization from the 95% confidence interval reported by the February CDC report cited above (19.1% ± 3.8%) hospitalizations).

How many hospital beds will they need to set aside to house the maximum plausible number of COVID-19 patients?

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.038

The provided estimate of proportion p is, p = 0.191
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.191*(1 - 0.191)*(1.96/0.038)^2
n = 411.08

Therefore, the sample size needed to satisfy the condition n >= 411.08 and it must be an integer number, we conclude that the minimum required sample size is n = 412
Ans : Sample size, n = 412 or 411