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An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 334 people living in East Vancouver and finds that 43 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should she take to achieve this?

Respuesta :

Answer:

The sample should be as large as 480

Step-by-step explanation:

Probability of having a flu, p = 43/334

p = 0.129

Margin Error, E = 0.03

Confidence Interval, CI= 95%

At a CI of 95%, [tex]z_{crit} = 1.960[/tex]

The sample size can be given by the relation:

[tex]n = p(1-p)(z/E)^{2}[/tex]

[tex]n = 0.129(1-0.129)(1.960/0.03)^{2} \\n = 479.59\\n = 480[/tex]

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