Review for Midterm 3

• Time and Places of Exam : In class, from 1:15pm to 2:30pm on Nov 17, 2005
  
  
• Exam Materials : The exam is closed book. You can prepare a formula sheet: a single 8x11 sheet on which you can write whatever you like. Normal table, t-table, and formula sheets (like this) are attached to the exam. You should bring a calculator.
  
  
• Exam Coverage : Here is a outline of required concepts and skills.
  

  Chap 6.1: Point Estimation

  • Differences between point estimator (a random variable) and point estimate (a number calculated from a sample).
  • Unbiased estimators. How to show an estimator is biased or unbiased?
  • How to calculate the variance (or standard deviation) of an estimator?
  • How to derive MLE? How to use the invariance principle to derive MLE for functions of parameters?
  • Exclude "The Method of Moments" (pp 269-271)

  Chap 7.1-7.3: Confidence Intervals (CI)

  • How to construct a CI for a population mean and proportion?
  • How to interpret a CI?
  • How is the width of a CI affected by sample size and significant level?
  • Given the width of CI, how to calculate the required sample size or the corresponding confidence level?
  • Know how to use the t-table.
  • For CIs for population proportion, use eq (7.11) instead of (7.10).
  • Exclude (1) one-sided CIs; (2) prediction intervals; (3) tolerance intervals; (4) Chap 7.4.

  Chap 8.1-8.4: Hypotheses Testing

  • Null and alternative hypotheses, rejection region, significant level, and P-value.
  • Type I and type II error. What is the relationship between type I error and significant level? How to calculate type II error for one-sided and two-sided test?
  • Test procedures for population mean and proportion.
  • How to determine the rejection regions (or how to calculate P-values) for upper-tailed, lower-tailed, and two-tailed tests?
  • Connection between two-tailed tests and confidence intervals.
  • Exclude (1) sample size determination (based on type II error) type of calculation; (2) small-sample test for population proportion on pp 342; (3) chap 8.5.

Everyone has their own approaches to study, but here are some (unsolicited) advice:
(1) Go over the lecture notes and textbook.
(2) Go through the outline of concepts above and make sure you understand them all.
(3) Can you do the homework assignments without looking at the solution?
(4) Do you understand all the examples covered in lecture and in textbook?