Chapter 6: Estimation of Proportion
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Estimation of Population Proportion

The sampling distribution of proportion for a large sample is approximately normal with

 

and .

A sample of 81 KSU students finds that 27 attend 3 or more Braves games each summer. Find a 95% confidence interval for the true population proportion of KSU students that attend 3 or more Braves games each summer.

 

 

 

 

 

A random sample of 140 KSU students finds that 113 of those students polled avoid classes that start before 9:30 AM.  Construct a 99% confidence interval for the true population proportion of students who avoid classes that start before 9:30 AM.

 

 

 

 

Chipper Jones hit .325 during the regular season. During a playoff games Chipper comes up to bat with the bases loaded and the announcers point out that Chipper had 20 hits in 49 at bats with the bases loaded during the regular season.  The announcers infer that Chipper is better at the plate when the bases are loaded than in general.  At a 99% level of confidence, are the announcers correct or is this just an example of chance variation?

 

 

 

The minimum sample size needed to estimate a population proportion with a fixed level of confidence and maximum error E is given by

 

.

 

Previous data indicates that 70% of any given 3:30 PM KSU class consists of traditional students.  Find the minimum sample size needed to be 95% confident that the new sample estimate percentage differs from the current population percentage by no more than 4%.

 

 

 

Should no previous estimate be available then

.

 

 

A national electronics chain wishes to estimate the percentage of its customers who would pay a yearly membership fee in order to receive a 15% discount on all purchases of books, CD's, DVD's, games and software.  Find the sample size needed to ensure that the sample estimate differs from the true population percentage by no more than 2.5%.  Test at 95% confidence.





Homework

Section 6-2:  27, 28, 30, 32-36

Syllabus Files ] Tips for Success ] Intro ] Chapter 2: Numerical Methods ] Chapter 3: Probability ] Chapter 4: Probability Distributions ] Chapter 5: The Normal Curve ] Chapter 5: Central Limit Theorem ] Chapter 4: The Binomial Probability Distribution ] Questionnaire ] Chapter 1 ] Chapter 6: Confidence Intervals ] Chapter 6: Required Sample Size ] [ Chapter 6: Estimation of Proportion ] Required Sample Size (Updated) ] Chapter 7: Hypothesis Testing ] Chapter 7: Applications of Hypothesis Testing ] Sample Tests ]