Chapter 10
Section 5
Putting It All Together:
Which Method Do I Use?
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 1 of 12
Chapter 10 – Section 5
● Learning objectives
1

Determine the appropriate hypothesis test to perform
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 2 of 12
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 tdistributions
 Both have means with known σ, means with unknown
σ, proportions, and standard deviations cases
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 3 of 12
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?
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 4 of 12
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 5 of 12
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
x  0

n
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 6 of 12
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
x  0
s
n
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 7 of 12
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)
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 8 of 12
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
p̂  p0
p0 ( 1 p0 )
n
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 9 of 12
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)
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 10 of 12
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?
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 10 Section 5 – Slide 11 of 12