Question

1. This problem has 4 parts. This is part 1 of 4.

   A random sample of 724 COVID-19 patients in the U.S. aged 20-44 had a hospitalization rate of 17.7%.

   Construct a 99% confidence interval for the population proportion of U.S. COVID-19 patients in this age group who require hospitalization.

   (Complete all calculations in Excel. Type your final interval below by giving the lower endpoint and upper endpoint. Give your answers as decimals, not percents. Round each endpoint to 4 decimal places.)

   Answer:

   Lower endpoint =

   Upper endpoint =

2. Write a sentence that interprets your interval from part 1. Your sentence should be phrased in the context of this scenario.

3. A journalist makes the following claim: “One in 4 U.S. patients with COVID-19, age 20-44, will require hospitalization.” The stated ratio “1 in 4” is the same as 25%. Based on the interval you found previously, is it reasonable to claim that the hospitalization rate for this age group is 25%? Briefly explain your answer.

4.Another journalist says the ratio is closer to 1 in 6, which is about 16.7%. Would this proportion be plausible? Explain your answer using the interval you found previously.

Answer 1

For critical value I used: =-NORM.INV((1-D7)/2,0,1)

For the margin of Error I used: =D8*SQRT(D5*D6/D4)

Lower Bound: =D5-D9

Upper Bound: =D5+D9

2. We're 99% confident that the true proportion of U.S. COVID-19 patients in this age group who require hospitalization lies in this interval.

3. No, it is not reasonable to claim that the hospitalization rate for this age group is 25% because 0.25 doesn't lie in the above confidence interval.

4. Yes, this proportion is plausible as this lies in the above confidence interval.