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.

Required:

Using the most conservative estimate, what sample size would be required to reduce the margin of error to 2 percentage points?

The sample size required is 2188.

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

The margin of error for this interval is:

The information provided is:

X = 162

n = 462

MOE = 0.02

Assume the confidence level as 95%.

Compute the sample proportion as follows:

The z-critical value for 95% confidence interval is:

Compute the sample size required as follows:

Thus, the sample size required is 2188.

fwms@lil_ben06

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc