SCCC 312A -- FINAL EXAM REVIEW SHEET

I.  Introduction to Inference
 A. What is Inference?
 B. How is it different from descriptive data analysis?
 C. Types of Inference
   1. Estimation of a Parameter
     a.  Point Estimation
     b.  Unbiased statistic
     c.  Standard Error of a Statistic
     d. Interval estimate
   2. Confidence Intervals
     a.  Confidence Level
     b.  Confidence Coefficient
     c.  Margin of Error

II.  Confidence Intervals
 A. Precise Interpretation of a Confidence Interval
   1.  What does, for example, "95 percent confidence" mean exactly?
 B. Relationship among confidence level, sample size, and width of the CI
 C. Sample Size Determination
   1. Sample size for CI about mu
 D. Confidence Intervals about a Proportion
   1. Definition of Sample proportion (p-hat)
   2. Sampling Distribution of p-hat
   3. When is p-hat approximately normal (rules of thumb)?
   4. Classical (Wald) CI for p
   5. Sample size determination for CI about p
 E. Confidence Intervals about a Mean (when sigma unknown)
   1. Sampling distribution of "t-statistic" (t distribution)
   2. How is t distribution different from standard normal?
   3. Reading Table 6 to get critical t values
   4. Formula for CI for mu

III. Hypothesis Tests
 A.  Purpose of Hypothesis Testing
   1. Null and alternative hypotheses
     a.  Which one is "assumed" to be true before the test?
     b.  Which one are we "trying to prove" (seeking evidence for)?
   2. Precise definition of P-value
   3. What does p-value tell us about the evidence against H_0?
   4. Type I and Type II errors
   5. Significance level (alpha) for a hypothesis test
   6. How do we decide whether to reject H_0 (whether result is "significant")?
 B.  One-sample t-test
   1. Test statistic t*
     a. What distribution does t* have if H_0 is true? (degrees of freedom?)
   2. How do we find the p-value?
     a. One-sided alternative (>)
     b. One-sided alternative (<)
     c. Two-sided alternative (not equal)
     d. Reading Table 7
   3. Stating conclusions in terms of the variables in the problem
   4. Assumptions and Robustness of the t procedures
     a.  When can we safely use the t procedures?
 C.  Hypothesis Test About a Proportion
   1. Test Statistic z*
     a. What distribution does z* have if H_0 is true?
   2. Finding P-value (for each type of alternative)
   3. Stating conclusions in terms of the variables in the problem 

IV. Inference in Two-Sample Situations
 A. Paired (Dependent) Samples
   1. What kinds of studies yield paired data? (Examples)
   2. Key characteristic of paired (dependent) samples
   3. Performing Inference about the Mean of the Differences
   4. t-test about mu_d
   5. CI about mu_d
   6. How does the paired-data problem reduce to a one-sample problem?
 B.  Independent Sample Problems
   1.  Key difference between Independent Samples and Dependent Samples
   2.  Comparing Two Population Means
     a. Assumptions
   3.  CI for mu_1 - mu_2
   4.  t-test of H_0: mu_1 = mu_2
     a. test statistic t*
     b. Determining correct degrees of freedom
     c. Finding P-value and making correct conclusion
   5.  Comparing Two Proportions
     a.  Sampling distribution of p_1-hat - p_2-hat
     b.  Assumptions for the approximate normality to be valid
   6.  Hypothesis test of p_1 = p_2
     a. test statistic z*
     b. pooled sample proportion p-hat
     c. Finding P-value and making correct conclusion

V.  Miscellaneous
 A.  The relationship between Confidence Intervals and Two-sided Hypothesis Tests