Question

1. As a potential worldwide pandemic, avian influenza H5N1 (commonly called the bird flu) poses a serious health risk. As of January 24, 2012, there have been 583 human cases of this virus in the world. Of these cases, 344 resulted in death.(Source: http://www.who.int/csr/disease/avian_influenza/en/) 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 infected 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. Interpret the interval.

Answer 1

Solution :

Given that,

n = 583

x = 344

Point estimate = sample proportion = = x / n = 344/583=0.590

1 -   = 1- 0.590 =0.410

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.590*0.410) /583 )

E = 0.0335

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.590-0.0335 < p <0.590+ 0.0335

0.5565< p <0.6235

The 90% confidence interval for the population proportion p is : 0.5565,0.6235