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 5 or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 338 students are selected randomly from a list of all students enrolled at the college. Of these, 139 admit to having engaged in binge drinking.

1) Give a 95% confidence interval for the proportion of all students at this college who engage in binge drinking.

The confidence interval (±0.001) is from_ to _?

Explanation / Answer

The sample proportion is: p=139/338=0.41

The 95% confidence interval is:

p+/-z(0.95)*root over p(1-p)/n

=0.41+/-1.96*root over 0.41*(1-0.41)/338

=0.41+/-0.05

=(0.36,0.46)

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