Statistics and Hypothesis Testing
Statistics and Hypothesis Testing
Statistics and Hypothesis Testing
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Convert to a st<strong>and</strong>ard normal problem<br />
Y act ∣]<br />
− µ ∣∣∣∣<br />
Y ,0<br />
∣ σ Y<br />
Y act ∣]<br />
− µ ∣∣∣∣<br />
Y ,0<br />
∣ σ Y<br />
[<br />
Y act ∣]<br />
[<br />
− µ ∣∣∣∣ Y ,0<br />
Y act ∣]<br />
− µ ∣∣∣∣<br />
Y ,0<br />
= Pr Z < −<br />
+ Pr Z ><br />
H 0 ∣ σ Y<br />
H 0 ∣ σ Y<br />
[<br />
Y act ∣]<br />
[<br />
− µ ∣∣∣∣ Y ,0<br />
Y act ∣]<br />
− µ ∣∣∣∣<br />
Y ,0<br />
= Pr Z < −<br />
+ Pr Z < −<br />
H 0 ∣ σ Y<br />
H 0 ∣ σ Y Y<br />
= Φ H0<br />
(−<br />
act ∣)<br />
− µ ∣∣∣∣ Y ,0<br />
Y + Φ<br />
∣<br />
H0<br />
(−<br />
act ∣)<br />
− µ ∣∣∣∣<br />
Y ,0<br />
σ Y<br />
∣ σ Y = 2Φ H0<br />
(−<br />
∣<br />
[∣ ∣ ∣∣∣∣<br />
Y − µ ∣∣∣∣<br />
Y ,0<br />
p-value = Pr<br />
><br />
H 0 σ Y<br />
[<br />
= Pr |Z| > ∣<br />
H 0<br />
Y act ∣)<br />
− µ ∣∣∣∣<br />
Y ,0<br />
σ Y