2-sample problems - inference on parameters involving two populations

  • Population 1: π‘‹Β βˆΌΒ π‘“π‘‹(π‘₯)
  • Population 2: π‘ŒΒ βˆΌΒ π‘“π‘Œ(𝑦)

CI - Independent or Paired Samples

2 Independent Samples

sample size of 𝑋 andΒ π‘Œ may be different

𝑋

π‘Œ

𝑋1

π‘Œ1

𝑋2

π‘Œ2

…

…

𝑋n

π‘Œm

Paired Samples

sample size of 𝑋 andΒ π‘Œ are the SAME

Subject #

(𝑋,Β π‘Œ)

𝐷 = 𝑋 - π‘Œ

1

(𝑋1,Β π‘Œ1)

𝐷1 = 𝑋1Β - π‘Œ1

2

(𝑋2,Β π‘Œ2)

𝐷2 = 𝑋2Β - π‘Œ2

…

…

…

n

(𝑋n,Β π‘Œn)

𝐷n = 𝑋nΒ - π‘Œn