Question

You wish to estimate the proportion of students in your math class who got a flu vaccine last year. Without taking an initial sample, how many students should you include in your sample to arrive at a 95% confidence interval for the population proportion that has a margin of error of 0.013?

Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.013

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} = Z_{0.025}
= 1.96

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.96 / 0.013)^{2} * 0.5 * 0.5

= 5682.84

Sample size =5683

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