Transcript 9.7 Power Point

Chapter 9: Hypothesis
Testing
Section 7: Testing Differences of Two
Means or Two Proportions
(Independent Samples)
Large Samples (Independent)
Test Statistic

x1  x2   1   2 
z
1  2

n1
n2
2
2
Test Statistic
,1  2  0 as stated in the null hypothesis
 x1 = sample mean of data
 x2 = sample mean of data
  1 = standard deviation of data
  2= standard deviation of data
 n1 = sample size of data
 n2 = sample size of data
Example
 A consumer group is testing camp stoves. To test the
heating capacity of a stove, they measure the time
required to bring 2 quarts of water from 50°F to boiling.
Two competing models are under consideration Thirtysix stoves of each model were tested and the following
results are obtained.
 Model 1: x1 = 11.4 and s1= 2.5
 Model 2: x2 = 9.9 and s1 = 3
 Is there any difference between the performances of
these two models? Use a 5% level of significance and
find the p-value.
Small Samples (Independent)
Test Statistic
x1  x2
t
1 1
s

n1 n2
df = n1 + n2 – 2
n1  1s1  n2  1s2
2
s
n1  n2  2
2
Example
Two competing headache remedies claim
to give fast-acting relief. An experiment
was performed to compare the mean
lengths of times required for bodily
absorption of brand A and brand B
headache remedies. Groups were
randomly selected to use the remedies.
Results (in minutes) are as follows:
Example
Brand A
n1 = 12
x1 = 20.1
s1 = 8.7
Brand B
n2 = 12
x2 = 18.9
s2 = 7.5
Use a 5% level of significance to test the
claim that there is no difference in the
mean times required for bodily absorption.
Proportions
Test Statistic
z
r1  r2
pˆ 
n1  n2
r2
ˆ2 
p
n2
pˆ1  pˆ 2
pˆ qˆ pˆ qˆ

n1 n2
r1
ˆ1 
p
n1
qˆ  1  pˆ
Example
 In order to improve voter registration, reminders
are sent in the mail to citizens who are eligible to
register. To determine if this method will improve
voter registration, two groups are used in a
study. In the first group of 625 people, no
reminders are sent and 295 registered. In the
second group of 625 people, reminders are sent
and 350 registered. The county clerk claims that
the proportion of people to register was
significantly greater in the second group. Use a
5% level of significance to test the claim.