Review of Statistics

Standardization

Central Limit Theorem

Criteria for Point Estimator Unbiased Minimum Variance Absolute Efficiency Relative Efficiency

假設檢定(Hypothesis Testing) “A person is innocent until proven guilty beyond a reasonable doubt. ” 在沒有充分證據證明其犯罪之前, 任何人皆是清白的. 假設檢定 H 0: m = 50 cm/s H 1: m 50 cm/s Null Hypothesis (H 0) Vs. Alternative Hypothesis (H 1) One-sided and two-sided Hypotheses A statistical hypothesis is a statement about the parameters of one or more populations.

Errors in Hypothesis Testing 檢定結果可能為 Type I Error(a): Reject H 0 while H 0 is true. Type II Error(b): Fail to reject H 0 while H 0 is false.

Hypothesis Testing on m - Variance Known

Construction of the C. I. From Central Limit Theory, Use standardization and the properties of Z,

Summary Table of Influence Procedures for a Single Sample (I)

Summary Table of Influence Procedures for a Single Sample (II)

Goodness-of-Fit Test (II) If the population follows the hypothesized distribution, X 02 has approximately a chi-square distribution with k-p-1 d. f. , where p represents the number of parameters of the hypothesized distribution estimated by sample statistics. That is, Reject the hypothesis if

Contingency Table Test - The Problem Formulation (I) There are two classifications, one has r levels and the other has c levels. (3 pension plans and 2 type of workers) Want to know whether two methods of classification are statistically independent. (whether the preference of pension plans is independent of job classification) The table:

Contingency Table Test - The Problem Formulation (II) Let pij be the probability that a random selected element falls in the ijth cell, given that the two classifications are independent. Then pij = uivj, where the estimator for ui and vj are Therefore, the expected frequency of each cell is Then, for large n, the statistic has an approximate chi-square distribution with (r-1)(c-1) d. f.