Question

As another potential worldwide pandemic, avian influenza H7N9 (commonly called the bird flu) poses a serious health risk. As of September 5, 2018, there have been 1567 confirmed human cases of this virus in the world (so far, all but three of these cases have occurred in China). Of these cases, at least 615 have resulted in death. Consider the outcomes of these cases as a random sample of all possible outcomes.

a. Find a point estimate for the proportion of people who would die if inflected with the bird flu.

b. Construct a 90% confidence interval for the proportion of cases that would be expected to result in death if a pandemic occurred.

c. Interpret the confidence interval (i.e., what does your confidence interval tell you?)

Answer 1

Solution :

Given that,

n = 1567

x = 615

a) Point estimate = sample proportion = = x / n = 615 / 1567 = 0.392

  1 - = 1 - 0.392 = 0.608

b) At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.392 * 0.608) / 1567 )

= 0.020

A 90% confidence interval for population proportion p is ,

± E  

= 0.392 ± 0.020

= ( 0.372, 0.412 )

c) We are 90% confident that the true proportion of cases that would be expected to result in death if a pandemic occurred between 0.372 and 0.412