Below is the observed cell frequencies (fij) in the K × 2 table: # Successes # Failures Total Sample 1 Y1 ni – Y1 ni Sample 2 Y2 n2 – Y2 n2 - Sample K YK пк - Үк | Under Ho : Pi = P2 =..PK = Po, it is expected to see the following cell frequencies (eij): # Successes # Failures Total Sample 1 nipo п (1 — ро) Sample 2 n2Po n2(1 – po) n2 Sample K NKPO пк (1 — Ро) NK к 2 K Show that lij- eij)² Cij (Y; – n;po)² Σ паро (1 — ро) i=1 j=1 i=1

MATLAB: An Introduction with Applications
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Below is the observed cell frequencies (fij) in the K x 2 table:
# Successes # Failures
Total
Sample 1
Y1
ni – Y
n1
Sample 2
Y2
n2 – Y2
n2
Sample K
YK
NK – YK
(a) Under Ho : P1 = P2 = ..PK = Po, it is expected to see the following cell frequencies (eij):
# Successes
# Failures
Total
пi (1 — ро)
п2(1 — Ро)
Sample 1
nipo
n1
Sample 2
n2Po
n2
Sample K
nK Po
пк (1 — ро)
к 2
Show that (Sij – eij)²
Cij
K
(fij – eij)?
(Y; – nipo)?
Σ
паро(1 — Ро)
|
i=1 j=1
(b) Under Ho : P1 = P2 = ..·pK, it is expected to see the following cell frequencies:
%3D
# Successes # Failures Total
Sample 1
nip
п (1 — р)
Sample 2
n2(1 – p)
n2
Sample K
пк(1 —р)
к 2
K
n;f)?
– nip)²
(Yi -
n;p(1 – p)
Show that E
(fij – Cij)²
-
Eij
i=1 j=1
i=1
Transcribed Image Text:Below is the observed cell frequencies (fij) in the K x 2 table: # Successes # Failures Total Sample 1 Y1 ni – Y n1 Sample 2 Y2 n2 – Y2 n2 Sample K YK NK – YK (a) Under Ho : P1 = P2 = ..PK = Po, it is expected to see the following cell frequencies (eij): # Successes # Failures Total пi (1 — ро) п2(1 — Ро) Sample 1 nipo n1 Sample 2 n2Po n2 Sample K nK Po пк (1 — ро) к 2 Show that (Sij – eij)² Cij K (fij – eij)? (Y; – nipo)? Σ паро(1 — Ро) | i=1 j=1 (b) Under Ho : P1 = P2 = ..·pK, it is expected to see the following cell frequencies: %3D # Successes # Failures Total Sample 1 nip п (1 — р) Sample 2 n2(1 – p) n2 Sample K пк(1 —р) к 2 K n;f)? – nip)² (Yi - n;p(1 – p) Show that E (fij – Cij)² - Eij i=1 j=1 i=1
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