1. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 1 of 11 Chapter 9 Section 4 Putting It All Together: Which Procedure Do I Use?

2. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 2 of 11 Chapter 9 – Section 4 ●Learning objectives  Determine the appropriate confidence interval to construct 1

3. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 3 of 11 Chapter 9 – Section 4 ●There are three different confidence interval calculations covered in Chapter 9 ●It can be confusing which one is appropriate for which situation ●I should use the normal … no, the t … no the … ???

4. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 4 of 11 Chapter 9 – Section 4 ●The one main question right at the beginning ●Which parameter are we trying to estimate?  A mean?  A proportion? ●This the single most important question

5. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 5 of 11 Chapter 9 – Section 4 ●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 Student's t-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 Student's t-distribution ●We don’t have to ask this question in the analysis of proportions

6. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 6 of 11 Chapter 9 – Section 4 ●For the analysis of a population mean ●If The data is OK (reasonably normal) The variance is known then we can use the normal distribution (section 9.1) with a confidence interval of to

7. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 7 of 11 Chapter 9 – Section 4 ●For the analysis 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 9.2) with a confidence interval of to

8. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 8 of 11 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. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 9 of 11 Chapter 9 – Section 4 ●For the analysis of a population proportion ●If n p (1 – p) ≥ 10 n ≤.05 N then we can use the proportions method (section 9.3) with a confidence interval of to

10. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 10 of 11 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. Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 11 of 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?