A national health organization warns that 30% of middle school students nationwi

Question

A national health organization warns that 30% of middle school students nationwide have been drunk. Concerned, a local health agency randomly and anonymously surveys 110 of the middle 1212 middle school students in its city. Only 21 of them report having been drunk. Show your work AND report your answer for both components below.

a) Create a 95% confidence interval for the proportion of the city’s middle school students who have been drunk.

b) To keep the margin of error at most 5%, how many middle school students do we need to survey? Assume we have no prior idea what the true proportion is.

Explanation / Answer

a)

alpha = 1 -0.95 = 0.05

alpha / 2 = 0.025

Z= 1.96

I : 0.30 +/- 1.96 * srqt ( 0.30*0.70 / 110 )

0.30 +/- 0.0856

0.2144 < p < 0.3856

b)

margin of error = 0.05

p = 0.50

n = [ 1.96^2 * 0.5 * 0.50 ] / 0.05^2

n = 384.16

n = 385

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