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Chapter 8: Q.2.3 (page 490)

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.

Short Answer

Expert verified

The confidence interval is(0.21764,0.23834).

Step by step solution

01

Given Information

Given that

Number of students (n)=10904

Number of binger drivers(x)=2486

Confidence level=99%

02

Explanation

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

CI=p^±za/2×p^(1-p^)n

Where,p^=xn

p^=xn

03

Calculation

From the standard normal table, the Z-score at99% confidence level is calculated as:

za/2=z0.10/2

=2.576

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

Therefore, the99%confidence interval is(0.21764,0.23834).

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Most popular questions from this chapter

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student-athletes concerning their gambling-related behaviors.17Of the 5594Division I male athletes in the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1% margin of error.

(a) The confidence level was not stated in the report. Use what you have learned to find the confidence level, assuming that the NCAA took an SRS.

(b) The study was designed to protect the anonymity of the student-athletes who responded. As a result, it was not possible to calculate the number of students who were asked to respond but did not. How does this fact affect the way that you interpret the results?

How common is SAT coaching? A random sample of students who took the SAT college entrance examination twice found that 427of the respondents had paid for coaching courses and that the remaining 2733 had not. 1+ Construct and interpret a 99% confidence interval for the proportion of coaching among students who retake the SAT. Follow the four-step process.

What critical value t⋆from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of t⋆. What advantage does the more accurate df provide?

What inference method will you use? Check that the conditions for using this procedure are met.

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