Question

Broome county’s health department hires you to analyze data on COVID-19. They come to you with data from your county’s local hospitals, and tell you that they have randomly tested 147 people showing symptoms of coronavirus. Results showed that 68 of those were positive for the virus. They are worried about running out of room in their hospitals, so they want you to estimate the true proportion of people with the virus.

a) The county officials are saying that based on initial results they believe about 46.3% of their county could have COVID-19. Explain to them why this is incorrect by defining the point estimate in this scenario and the parameter it is estimating. Give an estimate for the parameter in the form of a 90% confidence interval.

b) The county now wants a 90% confidence interval for the parameter with a margin of error of 0.05. How many total people will have to be tested before that can be achieved?

c) A neighboring county, Tioga, has 21 confirmed cased of the 55 that were tested in their hospitals similarly to how Broome county was sampled and tested. Estimate the true difference in proportions for these two counties using a 90% confidence interval.

Answer 1