1. Putting It All Together: Which Method Do I Use?
Chapter 10 Section 5
Putting It All Together:
Which Method Do I Use?

2. Chapter 10 – Section 5 Learning objectives
Determine the appropriate hypothesis test to perform 1

3. Chapter 10 – Section 5
Parallels between hypothesis tests and confidence intervals
Both use the concept of the variability of a sample statistic
Both use critical values from the normal Student’s t-distributions
Both have means with known σ, means with unknown σ, proportions, and standard deviations cases
Parallels between hypothesis tests and confidence intervals
Both use the concept of the variability of a sample statistic
Parallels between hypothesis tests and confidence intervals
Both use the concept of the variability of a sample statistic
Both use critical values from the normal Student’s t-distributions

4. Chapter 10 – Section 5
It should not be surprising that the decision process for which hypothesis test to use is very similar to the decision process for which confidence interval to use
Start with
Is the parameter a mean?
Is the parameter a proportion?
It should not be surprising that the decision process for which hypothesis test to use is very similar to the decision process for which confidence interval to use

5. Chapter 9 – Section 4 In analyzing population means
Is the population variance known?
If so, then we can use the normal distribution
If the population variance is not known
If we have “enough” data (30 or more values), we still can use the normal distribution
If we don’t have “enough” data (29 or fewer values), we should use the t-distribution
We don’t have to ask this question in the analysis of proportions
In analyzing population means
Is the population variance known?
If so, then we can use the normal distribution
In analyzing population means
Is the population variance known?
If so, then we can use the normal distribution
If the population variance is not known
If we have “enough” data (30 or more values), we still can use the normal distribution
If we don’t have “enough” data (29 or fewer values), we should use the t-distribution

6. The data is OK (reasonably normal)
Chapter 10 – Section 5
For the test of a population mean If
The data is OK (reasonably normal)
The variance is known
then we can use the normal distribution (section 10.2) with a test statistic of

7. Chapter 10 – Section 5 For the test of a population mean If
The data is OK (reasonably normal)
The variance is NOT known
then we can use the Student’s t-distribution (section 10.3) with a test statistic of

8. Chapter 9 – Section 4 For the analysis of a population mean If
The data is “strange”
(i.e. not normal at all)
then we should use nonparametric methods (not covered in this textbook)

9. Chapter 10 – Section 5 For the test of a population proportion If
n p (1 – p) ≥ 10
n ≤ .05 N
then we can use the proportions method (section 10.4) with a test statistic of

10. Chapter 9 – Section 4 For the analysis of a population proportion
If either
n p (1 – p) is too small (less than 10) or
n is too small (less than .05 N)
then we need to use some other method (not covered in this textbook)

11. Summary: Chapter 9 – Section 4
The main questions that determine the method
Is it a
Population mean?
Population proportion?
In the case of a population mean, we need to determine
Is the population variance known?
Does the data look reasonably normal?