Download Forming the Null and Alternative Hypotheses

Null Hypotheses
And
Alternate Hypotheses
Hypothesis Testing
Hypotheses are always about the population and never about the sample.
The true value of a hypothesis can never be known or confirmed.
Conclusions regarding hypotheses are never absolute and as such are
susceptible to some degree of definable/calculable risk of error.
Type I Error
Type II Error
Rejecting H0 when H0 is True
Failing to Reject H0 when H0 is False
Probability of Type I Error = α
Probability of Type II Error = β
Power of the Test
Probability of Correctly Rejecting a False Null Hypothesis = 1 - β
Probability of Correctly Rejecting H0 when H1 is true = 1 - β
Probability of Rejecting H0 when H0 is False = 1 - β
Probability of Accepting H1 when H1 is True = 1 - β
Probability of Type I and Type II Errors
The Level of Significance α establishes the Probability of a Type I Error.
The Probability of a Type II Error depends on the magnitude of the
true mean and the sample size.
Probability of Type II Errors
Consider
H0: μ = μ0
H1: μ ≠ μ0
Suppose the null hypothesis is false and the true magnitude of the
mean is μ = μ0 + δ.
X  0
X  0  
X  (0  )  n

Z0 





 n
 n
 n
 n
and therefore , Z0
 n 
N 
, 1 that is to say
 

Z0 is normally distributed with mean  n and variance 1.

Probability of Type II Error

 n
    Z 

 2


 n
     Z 
2






Applied Statistics and Probability for Engineers, 3ed, Montgomery & Runger, Wiley 2003