Question

The CDC would like to determine the proportion of individuals who are actively carrying the Corona virus. They take swabs from a random sample of 5,000 individuals and 118 have signs of the Corona virus. If more than 2% of the population have the virus more funds will be allocated to the virus. Based on a 90% confidence interval, do we have evidence that more funds need to be allocated to the virus?

Answer 1

n=5000, x=118, c=90%

formula for confidence interval is

Where Zc is the z critical value for c=90%

using z table we get

Zc = 1.645

0.02007 < P < 0.02713

Thus we get confidence interval as ( 0.02007 , 0.02713)

If more than 2% ( 0.02 ) of the population have the virus more funds will be allocated to the virus.

here, more than 2% ( 0.02 ) of the population have the virus, because lower bound of the confidence is above 0.02.

Hence, we have evidence that more funds need to be allocated.