According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and

Question

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in “binge drinking” behavior, having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking. Using your estimate for , what sample size would be required to reduce the margin of error to 2 percentage points? 2017 2187 2401 4802

Explanation / Answer

Sol:

estimate=sample proportion=p^=x/n=162/462=0.3506

1-p^=1-0.3506=0.6494

Z crit for 5%=1.96

E=0.02

WE HAVE

n=p^*q^(Zalpha/2/E)^2

=0.3506*0.6494*(1.96/0.02)^2

=2186.6

=2187

OPTION B

2187

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