Bell Ringer  The makers of Aspro brand aspirin want to be sure that their tablets contain the right amount of active ingredient (acetylsalicylic acid). So they inspect a random sample of 36 tablets from a batch of production. When the production process is working properly, Aspro tablets have an average of 320 mg of active ingredient. Here are the amounts (in mg) of active ingredient in the 36 selected tablets:  Calculate a 95% confidence interval to determine if you believe the content of active ingredient is correct in this batch of Aspro.

SECTION 8.2 Confidence Intervals for Proportions

Standard Error for proportions

Similar to confidence intervals for µ.  Conditions are the same.  How do we check normality?  The name of this procedure is a one-proportion z- interval.

Example  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 US college students collected information on drinking behavior and alcohol-related problems. The researchers defined “frequent binge drinking” as having five or more drinks in a row three or more times in the past two weeks. According to this definition, 2,486 students were classified as frequent binge drinkers. Calculate a 99% confidence interval for this situation.

Example  A random sample of students who took the SAT college entrance examination twice found that 427 of the respondents had paid for coaching courses and that the remaining 2733 had not. Construct and interpret a 97% confidence interval for the proportion of coaching among students who retake the SAT.

Margin of Error  Margin of Error: z*(SE) = z*  You can plan for your study by having enough observations to guarantee a predetermined margin of error.  If you know what p is expected to be, you can use that value.  If not, you can use.5 as long as you have good evidence (CI) that p is between.3 and.7

Example  A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that 70% of the student body would respond favorably. What sample size is required to obtain a 90% confidence interval with an approximate margin of error of 0.04? Suppose that 50% of the sample responds favorably?

p. 494 Check Your Understanding

Means or Proportions  Means  It will be stated  You have quantitative data  Proportions  You have some number out of a total SRS  You have categorical data

p. 496 (34, 36, 44, 50, 51, 52) Homework