1. Inference Sample Statistic Population Parameter
Hypothesis/Significance Testing
assess evidence the data gives against a hypothesis about a parameter
Confidence Regions
provide a range (region) believed to contain the parameter with a certain believability (confidence)
Confidence Intervals

2. The Scientific Method Make Observation Construct Hypothesis
Make Predictions from Hypothesis
Gather Observations / Experiment
Compare Observations to Predictions
Match, gain belief in hypothesis
Don’t match, lose belief in hypothesis
Inference Concepts

3. The Scientific Method Statistical hypothesis testing is at center
Compares predictions to observations in the face of sampling variability
Make Observation
Make Predictions from Hypothesis
Gather Observations / Experiment
Compare Observations to Predictions
Match, gain belief in hypothesis
Don’t match, lose belief in hypothesis
Construct Hypothesis
Statistical hypothesis testing follows same logic
Compares observations to predictions from a hypothesis
Inference Concepts

4. Two Main Hypothesis Types
Research Hypothesis
a general statement of an effect
Statistical Hypothesis (two types)
Alternative Hypotheses (HA)
a mathematical representation of the research hypothesis
one of HA: parameter <,>, specific value
Null Hypotheses (Ho)
the “no effect” or “no difference” situation
always Ho: parameter = specific value
Inference Concepts

5. What are the null and alternative hypotheses …
“The mean density of Canada yew (Taxus canadensis) in areas not exposed to Moose (Alces alces) on Isle Royale will be more than 1 stem per m2”
HA: m>1 vs. H0: m=1
Where m is the mean density of Canada Yew in ALL areas not exposed to Moose on Isle Royale.
Inference Concepts

6. What are the null and alternative hypotheses …
“The percentage of Ashland residents over the age of 40 whose parents were born in Ashland is greater than 35%.”
HA: p> vs. H0: p=0.35
Where p is the proportion of ALL Ashland residents over the age of 40 whose parents were born in Ashland
Inference Concepts

7. What are the null and alternative hypotheses …
“The mean age of medical college students (Homo sapien) is less than 24 years”
HA: m<24 vs. H0: m=24
Where m is the mean age of ALL medical college students.
Inference Concepts

8. What are the null and alternative hypotheses …
“The mean longevity of employees at the company is different than 10 years”
HA: m10 vs. H0: m=10
Where m is the mean longevity for ALL employees at the company.
Inference Concepts

9. What are the null and alternative hypotheses …
“A research paper claims that the mean fetal heart rate is 137 bpm. A doctor feels that the mean rate is lower for women admitted to her clinic.”
HA: m<137 vs. H0: m=137
Where m is the mean fetal heart rate for ALL pregnant women admitted to her clinic.
Inference Concepts