Q.2.3 - The Practice of Statistics for AP

Question

Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined “frequent binge drinking” as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers. 

Find the critical value for a 99% confidence interval. Show your method. Then calculate the interval. 

Step-by-Step Solution

Answer

$\text{ The confidence interval is }(0.21764,0.23834)\text{. }$

Step 1 Given Information

Given that

Number of students $\left(n\right)=10904$

Number of binger drivers $\left(x\right)=2486$

Confidence level$=99\%$

Step 2 Explanation

The formula to calculate the confidence interval for a population proportion is:

$CI=\hat{p}\pm z_{a/2}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where,$\hat{p}=\frac{x}{n}$

$\hat{p}=\frac{x}{n}$

Step 3 Calculation

From the standard normal table, the Z-score at$99\%$ confidence level is calculated as:

$z_{a/2}=z_{0.10/2}$

=2.576

The confidence interval using Ti-83 plus calculator is calculated as:

$\text{There fore , the }99\%\text{ confidence interval is }(0.21764,0.23834)\text{. }$