The sample size is necessary if the 95% ci for p is to have a width of at most 0.15 irrespective of p being 385 people.
In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time. Confidence intervals that include 95% or 99% of anticipated observations are frequently used by analysts.
The largest confidence interval occurs when p = .5
The standard error = [tex]\sqrt{\frac{(0.5)^{2} }{x} }[/tex]
The z* for a 95% confidence interval = 1.96
Setting up an equation,
[tex]1.96\sqrt{\frac{(0.5)^{2} }{x} } = 0.05[/tex]
Solving gives x=384.2.
So you need 385 people.
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