Cha10 要学的是:
1. involving two populations when the difference between the two population means or the two population proportions is of prime importance.
2. 例如:我们会学建立 interval estimate来看男性平均薪水和女性平均薪水之间的差异;或者建立一个 hypothesis test来看 供应商 A 和供应商 B 之间在 proportion 的差异。
10.1 Inferences About the Difference Between Two Population Means: σ1 and σ2 Known
Interval Estimation of μ1 - μ2
Hypothesis Tests about μ1 - μ2
案例:我们假设在两个 centers 之间没有差异。
所以:H0: μ1-μ2=0 Ha:μ1 - μ2 != 0
那么我们就可以计算 z = 1.66, 查表得出得出 0.9515,得到 p-value = 2*(1- 0.9515) = 0.0970, 这个大于0.05 level ,所以不 reject
10.2 Inferences About the Difference Between Two Population Means: σ1 and σ2 Unknown
Interval Estimation of μ1 - μ2
df = 47.8: We round the non integer degrees of freedom down to 47 to provide a larger t-value and a more conservative interval estimate.
Hypothesis Tests About μ1 - μ2
10.3 Inferences About the Difference Between Two Population Means: Matched Samples
案例:选择工人,测试方法一和方法二在效果上是否不同:
1. Sample Method:
1. Independent Sample Design: 分两批工人,一批方法一,一批方法二
2. Matched Sample Design:选出工人,对每个工人来说,先做一种方法,再做第二种方法 (第二种好一些)
所以,我们的 hypothesis变成了:
H0: μ(difference) = 0
Ha: μ(difference) != 0
然后再用之前做 t-test的方法来做,就能得到结果