Review of Statistics Standardization Central Limit Theorem Criteria

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.