STAT 515 -- EXAM 2 REVIEW SHEET 

I. Sample Variability and Sampling Distributions
 A.  Statistics and Parameters
   1.  Examples of each
   2.  What is the difference between a statistic and a parameter?
 B. Definition of a Sampling Distribution
   1. Estimation of a Parameter
     a.  Point Estimation
     b.  Unbiased statistic
     c.  Standard Error of a Statistic  
   2. Pattern of Variability of the Sample Mean Across Repeated Samples
   3. Mean of Sampling Distn. of X-bar
   4. Std. Deviation (Std. Error) of Sampling Distn. of X-bar
   5. Shape of Sampling Distn. of X-bar
     a.  When original data are normally distributed?  When data are not normal?
     b.  Central Limit Theorem (CLT)
     c.  When does the CLT apply?
 C.  Using the Sampling Distribution of the Sample Mean
   1.  Using Normal Distribution Techniques to Find Probabilities involving X-bar
 D. Other Sampling Distributions
   1. t-distribution
   2. Chi-square distribution
   3. F-distribution
   4. What are the shapes of these distributions?
   5. What do "degrees of freedom" signify for these distributions?
   6. Reading t, chi-square, and F tables in textbook

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. Small-sample 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 VI to get critical t values
   4. Formula for CI for mu
 D. Confidence Intervals about a Proportion
   1. Definition of Sample proportion (p-hat)
   2. Sampling Distribution of p-hat
   3. Classical CI for p
   4. When can we use this formula? (rules of thumb)
 E. Other Confidence Intervals
   1. Confidence interval for the variance sigma^2 (and for sigma)
 F. Sample Size Determination
   1. Sample size determination for CI about mu
   2. Sample size determination for CI about p

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. Type I error
   3. Significance level (alpha) for a hypothesis test
   4. 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. When do we reject H_0?
     a. One-tailed alternative (>)
     b. One-tailed alternative (<)
     c. Two-tailed alternative (not equal)
     d. Reading Table VI
   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. Determining rejection region (for each type of alternative)
   3. Stating conclusions in terms of the variables in the problem 
 D.  P-values
   1. Precise definition of P-value
   2. What does p-value tell us about the evidence against H_0?
   3. How to find p-values for tests about mu and about p

IV. Inference in Two-Sample Situations
 A. Paired Samples
   1. What kinds of studies yield paired data? (Examples)
   2. Key characteristic of paired 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 Paired Samples
   2.  Comparing Two Population Means
     a. Assumptions
     B. Equal-variance case and unequal-variance case
   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 rejection region 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 rejection region and making correct conclusion