Cha10 要學的是:
1. involving two populations when the difference between the two population means or the two population proportions is of prime importance.
2. 例如:我們會學建立 interval estimate來看男性平均薪水和女性平均薪水之間的差異;或者建立一個 hypothesis test來看 供應商 A 和供應商 B 之間在 proportion 的差異。
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:我們假設在兩個 centers 之間沒有差異。
所以:H0: μ1-μ2=0 Ha:μ1 - μ2 != 0
那麼我們就可以計算 z = 1.66, 查表得出得出 0.9515,得到 p-value = 2*(1- 0.9515) = 0.0970, 這個大於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:選擇工人,測試方法一和方法二在效果上是否不同:
1. Sample Method:
1. Independent Sample Design: 分兩批工人,一批方法一,一批方法二
2. Matched Sample Design:選出工人,對每個工人來說,先做一種方法,再做第二種方法 (第二種好一些)
所以,我們的 hypothesis變成了:
H0: μ(difference) = 0
Ha: μ(difference) != 0
然後再用之前做 t-test的方法來做,就能得到結果