Two-Sample Inference Procedures with Means
Suppose we have a population of adult men with a
mean height of 71 inches and standard deviation
of 2.6 inches. We also have a population of adult
women with a mean height of 65 inches and
standard deviation of 2.3 inches. Assume heights
are normally distributed.
 Describe the distribution of the difference
in heights between males and females
(male-female).
To simulate the sampling distribution of the
difference in means:
 Select a random sample of 30 men and record
their heights.
o Randnorm(71,2.6,30)  L1
o Find the sample mean for the mean
height of men
Example:
a) What is the probability that the mean height of
30 men is at most 5 inches taller than the mean
height of 30 women?
b) What is the 70th percentile for the difference
(male-female) in mean heights of 30 men and 30
women?
Purpose of two-sample procedures:
xM 

Select a random sample of 30 women and
record their heights.
o Randnorm(65,2.3,30)  L2
o Find the sample mean for the mean
height of women
Assumptions:
xW 

Find the find the difference in the sample
means
x M  xW 

Place your difference of means on the dot plot.

Repeat two more times
Degrees of freedom =
Option 1:
Looking at the sampling distribution of the
difference in sample means:
 What is the mean of the difference in sample
means?
x M  xW 
 What is the standard deviation of the
difference in sample means?
 x M  xW 
Option 2:
df 
2
s 2
 1  s2
n
n2
 1
s 2
 1
n1  1  n1

1




2

1

 n 
2

s 2
 2
1  n2





Formulas:
Difference between Matched Pairs and TwoSample Test:
Pooling?
Hypothesis Test Formulas:
Example: Two competing headache remedies
claim to give fast-acting relief. An experiment
was performed to compare the mean lengths of
time required for bodily absorption of brand A and
brand B. Assume the absorption time is normally
distributed. Twelve people were randomly
selected and given an oral dosage of brand A.
Another 12 were randomly selected and given an
equal dosage of brand B. The length of time in
minutes for the drugs to reach a specified level in
the blood was recorded. The results follow:
x
sx
n
Brand A
20.1
8.7
12
Brand B
18.9
7.5
12
 Describe the sampling distribution of the
differences in the mean speed of absorption.

Find a 95% confidence interval.
Example: Is there sufficient evidence that these
drugs differ in the speed at which they enter the
blood stream?
Robustness:
Example 3 - A modification has been made to the
process for producing a certain type of time-zero
film (film that begins to develop as soon as the
picture is taken). Because the modification
involves extra cost, it will be incorporated only if
sample data indicate that the modification
decreases true average development time by more
than 1 second. Should the company incorporate
the modification?
Original 8.6 5.1 4.5 5.4 6.3 6.6 5.7 8.5
Modified 5.5 4.0 3.8 6.0 5.8 4.9 7.0 5.7