Department of Mathematical Sciences

Binghamton University




Math 448, Introduction to Probability and Statistics II

List of Topics

BOOK: Mathematical Statistics with Applications by D. Wackerly, W. Mendenhall lII and R. L. Scheaffer, Fifth edition. Duxbury Press.

The numbers in parenthesis refer to section numbers in the book.

  1. Point Estimators ( 8.1)
  2. Mean and square error of point estimators ( 8.2)
  3. Several point estimators (8.3)
  4. Goodness of a point estimator (8.4)
  5. Confidence intervals (8.5)
  6. Asymptotic confidence intervals (8.6)
  7. Selecting the sample size (8.7)
  8. Confidence interval for the population mean and the difference of two population means (8.8)
  9. Confidence interval for the population variance (8.9)
  10. Relative efficiency (9.2)
  11. Consistency (9.3)
  12. Sufficiency (9.4)
  13. Minimum variance unbiased estimators (9.5)
  14. Method of the moments estimators (9.6)
  15. Maximum likelihood estimators (9.7)
  16. Asymptotics of the MLE's (9.8)
  17. Hypothesis testing (10.1)
  18. Elements of a statistical test (10.2)
  19. Common large sample tests (10.3)
  20. Calculating type II error probability and finding the sample size for the z test (10.4)
  21. Relationship between confidence intervals and hypothesis testing (10.5)
  22. P-values (10.6)
  23. Testing hypothesis concerning the population mean and the difference of two population means (10.8)
  24. Testing hypothesis concerning the population variance (10.9)
  25. Power of tests and the Neyman--Pearson lemma (10.10)
  26. Likelihood ratio tests (10.11)
  27. Linear statistical models (11.2)
  28. Method of least squares (11.3)
  29. Least squares estimators for the simple linear regression model (11.4)
  30. Inferences concerning the parameters of simple linear regression model (11.5)
  31. Predicting a particular value of Y using simple linear regression model (11.7)
  32. Correlation (11.8)
  33. Simple linear regression in matrix notation (11.10)
  34. Multiple linear regression model (11.11)-(11.14)
  35. Elements affecting the information in a sample (12.1)
  36. Designing experiments to increase accuracy (12.2)
  37. Matched pairs experiment (12.3)
  38. Elementary experimental designs (12.4)
  39. Analysis of variance procedure (13.2)
  40. Analysis of variance for a one-way layout (13.3)
  41. Analysis of variance table for a one-way layout (13.4)
  42. Estimation in the one-way layout (13.7)
  43. Chi-square test (14.2)
  44. A test of hypothesis concerning specified cell probabilities (14.3)
  45. Contingency tables (14.4)
  46. r x c tables (14.5)
  47. Sign test (15.3)
  48. Wilcoxon signed-rank test (15.4)
  49. Mann-Whitney U test (15.5)
  50. Kruskal-Wallis test (15.7)
  51. Friedamn test (15.8)
  52. Run test (15.9)