V-Sampling/Estimation-4

Question 1

definition:

simple random sampling

Answer 1

简单随机抽样

population中的每个个体都有相同几率被选入样本

Question 2

definition:

stratified random sampling

Answer 2

分层随机抽样

population is devided into several strata

从每个stratum中按比例随机抽取

Question 3

definition：

sampling error

Answer 3

the difference between sample statistics and population parameter

如：

sampling error of the mean =

sample mean - population mean

Question 4

definition:

Sampling Distribution of a Statistic

Answer 4

从总体中随机抽取的、样本大小相同的所有可能性样本的statistics的概率分布

Question 5

two different forms of data

Answer 5

Time-series data

Cross-sectional data

Question 6

Central Limit Theorem

实质

条件2

结论2

Answer 6

实质：就关于是所有样本的均值服从怎样的分布

条件：若n>=30， 且总体的均值、方差已知，

结论：则1。sampling distribution服从正态分布，

2。该正态分布的平均值等于总体均值，S²=σ²/n

Question 7

Standard Error

定义与实质

公式

Answer 7

标准差：样本均值分布的标准差。实质就是如果取n个数的样本，其描述的均值与总体均值的偏差，n越大偏差越小

know population variance:

σx = σ/根号n

unknown population variance:

sx = s/根号n

（即假设样本标准差就是总体标准差）

Question 8

estimator内涵

3 properties of a good estimator

Answer 8

• estimator: 即estimate formula, 一个计算方式，得出的是一组分布
• unbiasedness: 估计量期望值等于总体参数真实值。E(Xbar) = μ
• Efficiency: （在无偏估计量的基础上）方差最小
• Consistency: 随样本量增大，精确性增加，Standard Error变小

Question 9

2 approaches for

estimation

Answer 9

• Point Estimate: a single value estimates population parameter
• Confidence Interval Estimate: 总体参数落在某一区间的概率

Question 10

Confidence Interval Estimation:

公式

Answer 10

confidence interval: Xbar +- k·(σ/根号n)

[Point Estimate +/- k· Standard Error]

(根据normal distribution的置信区间，和central limit theorum推来)

Question 11

width of confidence interval

and

how to decrease width

Answer 11

sample variance 变小，

number of obervations增加

Question 12

definition:

Level of significance

Degree of Confidence

α

Answer 12

• 显著性水平/置信水平：1-95% = 5%
• 置信度：如“落在μ+-1.96标准差区间内的概率是95%”， 95%
• α： 5%

Question 13

Student t-distribution

图形及性质5点

Answer 13

1. skewness = 0 (symmetry)
2. platykurtic than normal distribution，fatter tail 矮峰肥尾
3. 变量：Degrees of freedom df = n-1
4. 自由度增加，图形收紧，峰变高，趋向于正态分布
5. 相同level of confidence水平下，t分布的置信区间比z分布要宽

Question 14

1. z分布,.t分布, .z-Alternative下的置信区间构建
2. reliable factor?

Answer 14

z-Alternative: large sample, unknown population variation

equation with z and s

2. reliable factor: 即Z value

Question 15

confidence interval estimation时，

何时选择z分布，何时选择t分布？

3点

Answer 15

• 方差已知用z，方差未知用t
• 大样本时即使未知方差也可用z（t已趋向于z）
• 非正态分布总体小样本：不可估计

Question 16

查z分布表和t分布表时

有何区别

Answer 16

t表需知degrees of freedom.

Question 17

影响confidence interval 宽度的因素

Answer 17

1. reliable factor: choice of z or t distribution; choice of degree of confidence
2. standard error: sample size

Question 18

what may be downsides of

bigger sample size?

Answer 18

1. 可能会使用observations from another population
2. 成本考虑

Question 19

5 types of bias

Answer 19

• Data-mining bias: 拿偶然当必然，取样与假设检验使用同一数据库。只具有统计学意义
• sample selection bias: 有些数据unavalable
• survivorship bias
• look-ahead bias: 分析当下没有该数据，预估未来数据
• time-period bias:太长或太短(–data mining)

Question 20

A statistically significant result might not be

economically meaningful if you account

Answer 20

the risk, transaction costs, and applicable taxes