Question

1. Section 9.1 Estimating a Population Proportion

Bird Flu:

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 have resulted in death. Consider the outcomes of these cases as a random sample of all possible outcomes.

1. Find a point estimate for the proportion of people who would die if infected with the bird flu. Construct a 90% confidence interval for the proportion of cases that would be expected to result in death if a pandemic occurred.
2. Interpret the confidence interval.

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Answer 1

a)

sample proportion, = 0.59
sample size, n = 583
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.59 * (1 - 0.59)/583) = 0.0204

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.0204
ME = 0.0335

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.59 - 1.64 * 0.0204 , 0.59 + 1.64 * 0.0204)
CI = (0.5565 , 0.6235)

b)

Therefore, based on the data provided, the 90% confidence interval for the population proportion is 0.5565 < p < 0.6235 , which indicates that we are 90% confident that the true population proportion p of cases that would be expected to result in death if a pandemic occurred.is contained by the interval (0.5565 , 0.6235)