When you have completed this chapter, you will be able to: Explain the the difference between dependent and independent samples, conduct a test of hypothesis and obtain a confidence interval estimate for the difference between two population means using independent samples and using matched pair sample.
Trang 21. Explain the the difference between dependent and
Trang 3and make a decision
Trang 4If both samples contain
at least 30 observations
we use the z distribution
as the test statistic.
We wish to know whether the the distribution of the
differences in sample
means has a mean of 0
We wish to know whether the the distribution of the differences in sample
means has a mean of 0
Trang 5The samples are from independent populations.The formula for computing the value of z is:
Trang 6The local paper recently reported that the
mean starting salary of a graduate
from College 1 is $38,000
with a standard deviation of $6,000 for a sample of 40 graduates.
The same article reported the
mean starting salary of a graduate from College 2 is $35,000 with a standard deviation of $7,000 for a sample of 35 graduates.
At the .01 significance level can we conclude the
mean salary of College 1 is more?
Trang 7Compute the test statistic and make a decision
Step 5
H0: µ1 = µ2
H1: µ1 > µ2 = 0.01
Because both samples are more than 30, the test statistic is Z
Reject H0 if z > 2.33
Do not reject the null hypothesis; insufficient evidence.
2
2 2 1
2 1
2 1
n s n
s
X X
($
40000)
,6
z
Trang 8than the chosen alpha of
0.01, there is insufficient
evidence to reject H0
1.98 0
Trang 9Small Sample Tests of Means Small Sample Tests of Means
If one or more of the samples contain
less than 30 observations we use
Trang 10) 1
(
2 1
2 2 2
2 1 1
Trang 11A sample of 15 domestic cars revealed a mean of
33.7 mpg with a standard deviation of 2.4 mpg.
A sample of 12 imported cars revealed a
mean of 35.7 mpg with a standard deviation of 3.9.
At the .05 significance level can the EPA conclude that the mpg is higher on the imported cars?
At the .05 significance level can the EPA conclude that the mpg is higher on the imported cars?
Trang 12Compute the test statistic and make a decision
Step 5
H0: µd = µ1
H1: µd < µ1 = 0.05
Because both samples are less than 30, the test statistic is t
) 1
(
2 1
2 2 2
2 1 1
Trang 13Compute the test statistic and make a decision
Compute the test statistic and make a decision
2
) 1 (
) 1
(
2 1
2 2 2
2 1 1
n s
.9
H0 cannot be rejected… insufficient evidence.
H0 cannot be rejected… insufficient evidence.
Trang 14same car at two (or more) different dealerships
and compare the prices.
If you wished to buy a car, you would look at the
same car at two (or more)
different dealerships and compare the
that are paired
or related
in same fashion
Dependent samples are samples
that are paired
or related
in same fashion
Trang 15…is the mean of the differences
Trang 16is comparing the daily rental cost for renting a compact car from Hertz and Avis.
Trang 17Compute the test statistic and make a decision
Step 5
H0: µD = 0
= 0.05
Because both samples are less than 30, the test distribution is t
Trang 18D D 2
Compute the test statistic and make a decision
Compute the test statistic and make a decision
4162
05
3 2
4
40259 416Solution continues…
n
sD /
Trang 19D D
8
0
8 78
n
sD /
Trang 201
n n
X X
ˆp
2 1
1 )
ˆ 1
(
ˆ
n n
p p
Trang 21Are unmarried workers more likely to be absent from work than married workers?
Trang 22Compute the test statistic and make a decision
Step 5
= 0.05
Because both samples are large the z distribution is used
Reject H0 if z > 1.645
Solution continues…
H1: Pu Pm
21
21
ˆ
n n
X
X
p
H0: pu p= m
Trang 23Compute the test statistic and make a decision
Compute the test statistic and make a decision
Step 5
2 1
1
n n
) ˆ 1
2 1
ˆ
n n
3001 .1036)
(.1036
25022
30035
= 1.10
Trang 25searchable glossary access to Statistics Canada’s EStat data
…and much more!
Trang 26This completes Chapter 11