1. Inference Concepts
Hypothesis Testing

2. Summary (from Before)
Make statistical hypotheses from research hypothesis
Use H0 to make prediction (Assume H0 is true)
this is why H0 must be the “equals” situation
Compare predicted statistic to observed statistic
calculate p-value
Compare p-value to rejection criterion (a)
if p-value > a then DNR H0
conclude that H0 could be correct
if p-value < a then reject H0
conclude that H0 is probably not correct
Critical
Inference Concepts

3. if p-value > a then H0 could be correct
Recall that `x = 135.9
for H0: m=137, p-value=0.1357, DNR H0
for H0: m=137.1, p-value=0.1151, DNR H0
for H0: m=137.2, p-value=0.0968, DNR H0
for H0: m=137.3, p-value=0.0808, DNR H0
There are always several other hypotheses that would also not be rejected.
distrib(135.9,mean=137,sd=10/sqrt(100))
distrib(135.9,mean=137.1,sd=10/sqrt(100))
distrib(135.9,mean=137.2,sd=10/sqrt(100))
distrib(135.9,mean=137.3,sd=10/sqrt(100))
Inference Concepts

4. DNR vs Accept
The data do not contradict this H0, but it is not fully known if this H0 is true.
Inference Concepts

5. if p-value < a then H0 is probably incorrect
Even if H0 is truly correct it is possible to observe a statistic in the tail, resulting in a p-value < a, and a rejection of H0.
137
138
139
140
136
135
134
Inference Concepts

6. Decision Making Errors
Set a priori by the researcher
Can’t be known, because truth is not known
Type I a
Correct
power
Ha mu<100, sigma-10,n=30,alpha=0.05
True mu=95
Type II b
Correct
Inference Concepts