STAT 513 -- EXAM 1 REVIEW SHEET 

I. Brief Introduction to Hypothesis Testing
  A.  Null Hypothesis and Alternative (research) Hypothesis
  B.  Type I and Type II errors in Hypothesis Testing 
     1. Rejection Region
     2. Significance Level: alpha
     3. P[Type II error]: beta
     4. Relationship between alpha, beta, and sample size
II. Common Large-Sample Z-tests
  A. General Form of Test Statistic
  B. Three Possible Alternatives
     1. Rejection regions for each alternative
  C. Specific Common Examples of z-tests
     1. Test about a Population Mean
     2. Test about a Population Proportion
     3. Test comparing Two Population Means
     4. Test comparing Two Population Proportions
III. Finding Type II Error Probabilities
  A. Finding P[Type II Error] with a z-test
  B. Finding P[Type II Error] with an exact binomial test
  C. Sample size formulas
IV. P-values
  A. Definition and Calculation of P-value
  B. Calculating P-values of z-tests (one-tail and two-tail)
  C. Calculating P-values of binomial test (one-tail)
  D. Approximating P-values of other tests (t, chi-square, F)
V.  Statistical Significance vs. Practical Significance
VI. Small-sample tests about mu and mu1 - mu2
  A. One-sample t-test (including appropriate assumptions)
  B. Rejection region for each of 3 alternatives
  C. Two-sample t-test (including appropriate assumptions)
    1. Pooled sample variance
    2. Rejection region for each of 3 alternatives
  D. Robustness of t-tests
VII. Tests about Variances
  A. One-sample chi-square test (including appropriate assumptions)
  B. Rejection region for each of 3 alternatives
  C. Two-sample F-test (including appropriate assumptions)
    1. Pooled sample variance
    2. Rejection region for each type of alternative
  D. Robustness of tests for variances (of lack thereof)
VIII. Power
  A. Power at a specific parameter value
  B. Power function
  C. Calculating power functions for z-tests
  D. Calculating power functions for binomial or other easy tests
  E. Definition of Most Powerful alpha-level test