Chapter 24 – Comparing Means
Boxplot of data
 Early in the semester, we used boxplots to compare
the distributions of different data sets.
 We will be using them here again when we compare
the means of different data sets.
 This will give us a quick visual as to what we should
be testing and whether or not there seems to be a
difference between the means.
Boxplots Example
Below are figures from the text representing the performance
of AA alkaline batteries from a major brand name and a
generic competitor.
Figures from DeVeaux, Intro to Stats
Sampling Distribution:
Difference Between 2 Sample Means
 When the conditions are met, the sampling distribution of
the standardized sample difference between the means of 2
independent groups,
y1  y2    1  2 

t
SE  y1  y2 
Can be found using a Student’s t-model with a number of
degrees of freedom found by a special formula. We
estimate the standard error with
s12 s22
SE  y1  y2  

n1 n2
Assumptions and Conditions
 Independence Assumption
 Randomization condition
 10% condition
 Normal Population Assumption
 Nearly Normal condition (check both groups)
 Independent Groups Assumption
 Can’t use related or matched pairs
Two-Sample t-Interval for Difference between Means
When the conditions are met, we are ready to find the confidence
interval for the difference between means of two independent
groups.
The confidence interval is
 y1  y2   t

df
 SE  y1  y2 
where the standard error of the difference of the means is
s12 s22
SE  y1  y2  

n1 n2
The critical value depends on the particular confidence level, C, that you
specify and on the number of degrees of freedom, which we get from the
sample sizes and a special formula.
Example: SSHA Test
 The Survey of Study Habits and Attitudes(SSHA)
was given to male and female first-year students in a
selected private school. Most of the studies suggest
that the mean SSHA score for men is lower than the
that in a comparable group of women. Is this true for
first-year students at this college?
 Let’s explore in Minitab using the dataset:
SSHA.mtw
Example: SSHA.MTW
 Generate histograms of each data set to see if the
Nearly Normal condition is met.
 Generate a boxplot to see if it looks like there is a
difference between each gender’s performance on the
test.
 Construct a 95% confidence interval using Minitab
 State your conclusion.
Two-Sample t-Test for Difference between Means
We test the hypothesis H0: 1 – 2 = 0, where the hypothesized
difference, 0, is almost always 0, using the statistic
y1  y2    0

t
SE  y1  y2 
The standard error is
s12 s22
SE  y1  y2  

n1 n2
When the conditions are met and the null hypothesis is true, this
statistic can be closely modeled by a Student’s t-model with a
number of degrees of freedom given by a special formula. We use
that model to obtain a P-value.
Example: Front vs. Back of the Class
 Hours spent studying per week are reported by students in
a class survey. The 99 students who sat in the front studied
an average of 16.4 hours per week with a standard deviation
of 10.85 hours. The 94 students who sat in the back studied
an average of 10.9 hours per week with a standard
deviation of 8.41 hours. Test the claim that the students in
the front of the class studied more on average than the
students in the back.
 Use Minitab to perform a hypothesis test. Make sure to
state your hypotheses before beginning the test.
Homework
 Chapter 24: 1, 7, 9, 11, 19, 25, 27, 33, 43
 Exam 3: Wednesday, 11/30
 Project 2: Due Monday, 11/28