Question

1. According to the National Institute on Alcohol Abuse and Alcoholism and the National Institute of Health, 41% of college students nation-wide engage in “binge drinking” behavior, that is having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is different than the national proportion.

In a commissioned study of her college only, 348 students are randomly selected from a list of all students enrolled at the college. Of these, 118 admit to having engaged in binge drinking.

1. Calculate the sample proportion of binge drinkers randomly selected at this college for this sample.

2. Check the two necessary conditions to determine if it is appropriate to use normal distribution calculations in this case for this proportion problem.

3. Assuming the conditions above are met, calculate a 90% confidence interval for the proportion of all students at this college that engage in binge drinking (show all work). Interpret your results. Use standard error = 0.025.

4. Given that the national proportion of college binge drinkers is 0.41, should this college president be concerned the proportion of binge drinkers at her college are higher than the national proportion? Explain. Hint: think about the confidence interval end points and determine if the national proportion of binge drinkers, 0.41, is in that interval.

Answer 1

Here, 118 out of 348 students admit to having engaged in binge drinking.

a)The sample proportion , = 118 / 348

= 0.34

b)The conditions are :

The sample size should be large. Here, sample size = 348 , hence it is sufficiently large.

The data must be sampled randomly , which is also met here.

c) Given , standard error = 0.25

z-value for 90% confidence interval = 1.645

The confidence interval is = z*(standard error)

= 0.34 0.041

=(0.299 , 0.381)

d) We see that, the population proportion , 0.41 is not included in this interval. In fact, the upper limit of this interval is less than the population proportion. Therefore, college president should not be concerned that the proportion of binge drinkers at her college are higher than the national proportion.