Download Two-Sample Inference Procedures with Means

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).
a) What is the probability that the height of a
randomly selected man is at most 5 inches taller
than the height of a randomly selected woman?
b) What is the 70th percentile for the difference
(male-female) in heights of a randomly selected man
& woman?
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
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
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
Looking at the sampling distribution of the
difference in sample means:
 What is the mean of the difference in sample
means?
x  x 
M
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:
Assumptions:
Formula for CI:
Degrees of freedom =
Option 1:
Option 2:
2
s 2
 1  s2
n
n2
 1
W
 What is the standard deviation of the
difference in sample means?
 x x 
M
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?
W
df 
s 2
 1
n1  1  n1

1




2

1

 n 
2

s 2
 2
1  n2





Hypothesis Test:
Pooling?
Robustness:
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.

Example: Is there sufficient evidence that these
drugs differ in the speed at which they enter the
blood stream?
Find a 95% confidence interval.
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
Modified
8.6
5.5
5.1
4.0
4.5
3.8
5.4
6.0
6.3
5.8
6.6
4.9
5.7
7.0
8.5
5.7