Central limit theorem
基本面： n>30, 样本均值=总体均值，样本方差=总体方差/N
standard error of the sample mean: standard deviation of the distribution of the sample means
= 总体标准差/N的根号
estimator: unbiased, efficient, & consistent
student's t-distribution
基本面
像个钟，mean=0
a single parameter (df)
less peaked and fatter tails
if N increase, 形状趋向正态分布
样本的数量是n-1
Confidence interval置信区间
alpha is level of significance. 1-alpha is degree of confience.
e.g. population mean of variables is 15-25 with 95% degree of confidence or 5%level of significance
formula = 样本均值 + - distribution x standard error
known population variance and normal distribution
Z-table
e.g. 1.65 for 90%confidence intervals is 10%degree of confidence & 5% on each tail.
unknown population variance and normal distribution
T-table,
n = N-1
nonnormal distribution with large sample
known variance - Z-table
Unknown variance - T-table & Z-table
Bias
data-mining bais: significant replationship that have occurred by chance
sample selection bias- non-random
survivorship bias - using only surviving funds
look-ahead bias -basing the test at a point in time on data not available at that time
time-period bias - the relation does not hold over other time period
