Question

1.   You survey 850 teenagers and find that 196 of them smoke cigarettes.
a.   What is the sample proportion?
b.   Write a 95% confidence interval for the proportion of teenagers who smoke cigarettes.
c.   Write a sentence interpreting this interval.
c.   What is the margin of error for this interval?
d.   Suppose we’d like the margin of error to be less than 1%? Using the same sample proportion from part a, how big of a sample would we need?

Answer 1

Ans:

a)

Sample proportion=196/850=0.2306

b)

95% confidence interval for p

=0.2306+/-1.96*sqrt(0.2306*(1-0.2306)/850)

=0.2306+/-0.0283

=(0.2023, 0.2589)

c)

We are 95% confident that population proportion of teenagers who smoke cigarettes falls within 0.2023 and 0.2589.

d)

Margin of error=1.96*sqrt(0.2306*(1-0.2306)/850)=0.0283

e)

Sample size required,n=1.96^2*0.2306*(1-0.2306)/0.01^2=6815.9

$n\approx 6816$