Question

a) An epidemiologist with the Florida Deparment of Health needs to esimate the proportion of Floridians who are infected with the corona virus but are asymptomatic (show no signs of the virus). The epidemiologist compiled a preliminary random sample of infected patients and found that 39% of the sample were also asymptomatic.

How large a sample should be selected such that the margin of error of the estimate for a 96% confidence interval is at most 1.96%. Round the solution up to the nearest whole number.

n=

b)COVID-19 (novel corona virus) took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected.

Early reports have claimed that a large percentage of those infected with the corona virus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them.

Suppose the U.S. Centers for Disease Control and Prevention (CDC) needs to estimate the proportion of the infected population that is also asymptomatic. A random sample of 1155 infected patients is examined and 197 are observed to be asymptomatic.

Determine the point estimate, ˆp and the sample standard deviation, sˆp. Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary.

ˆp=

sˆp=

Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the proportion of all patients who are infected with the corona virus and are also asymptomatic. Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.

The margin of error is given by E=.

A 99% confidence interval is given by _____

c)

The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 19% of all county residents held at least a bachelor's degree.

Find three different confidence intervals - one with sample size 380, one with sample size 589, and one with sample size 756. Assume that 19% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary.

• When n=380, the margin of error for a 95% confidence interval is given by .
  
  When n=380, a 95% confidence interval is given by .  
  
• When n=589, the margin of error for a 95% confidence interval is given by .
  
  When n=589, a 95% confidence interval is given by .  
  
• When n=756, the margin of error for a 95% confidence interval is given by .
  
  When n=756, a 95% confidence interval is given by .  

Answer 1