1. Review of Chapter 12 Significance Tests in Practice
Lesson 12 - R
Review of Chapter 12
Significance Tests in Practice

2. Objectives Conduct one-sample and paired data t significance tests.
Explain the differences between the one-sample confidence interval for a population proportion and the one-sample significance test for a population proportion.
Conduct a significance test for a population proportion.

3. Vocabulary
None new

4. Inference Toolbox Step 1: Hypothesis Step 2: Conditions
Identify population of interest and parameter
State H0 and Ha
Step 2: Conditions
Check appropriate conditions
Step 3: Calculations
State test or test statistic
Use calculator to calculate test statistic and p-value
Step 4: Interpretation
Interpret the p-value (fail-to-reject or reject)
Don’t forget 3 C’s: conclusion, connection and context

5. Reject null hypothesis, if
P-Value is the area highlighted
-tα
-tα/2
tα/2 tα t0
-|t0|
|t0| t0
Critical Region
x – μ0
Test Statistic: t0 =
s/√n
Reject null hypothesis, if
P-value < α
Left-Tailed
Two-Tailed
Right-Tailed
t0 < - tα
t0 < - tα/2 or
t0 > tα/2
t0 > tα

6. Confidence Interval Approach
x – tα/2 · s/√n x + tα/2 · s/√n
Lower Bound
Upper Bound μ0
Reject null hypothesis, if
μ0 is not in the confidence interval
P-value associated with lower bound must be doubled!

7. Using t-Test on Differences
What happens if we have a match pair experiment?
Use the difference data as the sample
Use student-t test statistic
With previously learned methods
xdiff – μ0
t0 =
sdiff / √n

8. Reject null hypothesis, if
P-Value is the area highlighted
-zα
-zα/2
zα/2 zα z0
-|z0|
|z0| z0
Critical Region
p – p0
Test Statistic: z0 =
p0 (1 – p0) n
Reject null hypothesis, if
P-value < α
Left-Tailed
Two-Tailed
Right-Tailed
z0 < - zα
z0 < - zα/2 or
z0 > zα/2
z0 > zα

9. Confidence Interval Approach
p – zα/2 ·√(p(1-p)/n p + zα/2 · √(p(1-p)/n
<
Lower Bound
Upper Bound p0
Reject null hypothesis, if
p0 is not in the confidence interval
P-value associated with lower bound must be doubled!

10. Are you prepared for the Test?

11. Summary and Homework Summary Homework
Remember the 4 steps of the Inference Toolbox
Three conditions for inference testing: SRS, Normality, and Independence
Test statistic format the same
Homework
pg 775 – 77; to 12.38
p – p0
z0 =
p0 (1 – p0) n
x – μ0
t0 =
s / √n