Matakuliah
Tahun
: L0104 / Statistika Psikologi
: 2008
Pengujian Hipotesis Nilai Tengah
Pertemuan 15
Learning Outcomes
Pada akhir pertemuan ini, diharapkan
mahasiswa akan mampu :
Mahasiswa akan dapat menyusun simpulan
dari langkah-langkah uji hipotesis nilai tengah
dan beda nilai tengah.
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Outline Materi
•
•
•
•
Uji nilai tengah sampel besar
Uji nilai tengah sampel kecil
Uji beda nilai tengah dua populasi bebas
Uji beda dua nilai tengah populasi tidak
bebas
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Hypothesis Testing
• Developing Null and Alternative Hypotheses
• Type I and Type II Errors
• One-Tailed Tests About a Population Mean:
Large-Sample Case
• Two-Tailed Tests About a Population Mean:
Large-Sample Case
• Tests About a Population Mean:
Small-Sample Case
continued
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Developing Null and Alternative
Hypotheses
• Hypothesis testing can be used to determine
whether a statement about the value of a population
parameter should or should not be rejected.
• The null hypothesis, denoted by H0 , is a tentative
assumption about a population parameter.
• The alternative hypothesis, denoted by Ha, is the
opposite of what is stated in the null hypothesis.
• Hypothesis testing is similar to a criminal trial. The
hypotheses are:
H0: The defendant is innocent
Ha: The defendant is guilty
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Developing Null and Alternative Hypotheses
• Testing Research Hypotheses
– The research hypothesis should be expressed as
the alternative hypothesis.
– The conclusion that the research hypothesis is
true comes from sample data that contradict the
null hypothesis.
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A Summary of Forms for Null and
Alternative Hypotheses about a
Population Mean
• The equality part of the hypotheses always appears in
the null hypothesis.
• In general, a hypothesis test about the value of a
population mean μ must take one of the following three
forms (where μ0 is the hypothesized value of the
population mean).
H0: μ > μ0
Ha: μ < μ0
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H0: μ < μ0
Ha: μ > μ0
H0: μ = μ0
Ha: μ ≠ μ0
Contoh Soal: Metro EMS
• Type I and Type II Errors
Conclusion
Accept H0
(Conclude μ <12)
Reject H0
(Conclude μ > 12)
Conclusion
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Population Condition
H0 True
Ha True
(μ < 12 )
(μ > 12 )
Correct
Conclusion
Type II
Error
Type I
Correct
Error
The Steps of Hypothesis Testing






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Determine the appropriate hypotheses.
Select the test statistic for deciding whether or not to
reject the null hypothesis.
Specify the level of significance  for the test.
Use to develop the rule for rejecting H0.
Collect the sample data and compute the value of the
test statistic.
a) Compare the test statistic to the critical value(s) in
the rejection rule, or
b) Compute the p-value based on the test statistic and
compare it to to determine whether or not to reject
H0.
One-Tailed Tests about a Population Mean:
Large-Sample Case (n > 30)

Hypotheses
H0:   
Ha: 

H0:   
Ha: 
Test Statistic
 Known
x  0
z
/ n

or
 Unknown
x  0
z
s/ n
Rejection Rule
Reject H0 if z > zReject H0 if z < -z
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Two-Tailed Tests about a Population
Mean:
Large-Sample Case (n > 30)
• Hypotheses
H0: μ =
Ha: μ≠
• Test Statistic
σ
z
μ0
Known
x  0
/ n
μ
σ Unknown
x  0
z
s/ n
• Rejection Rule
Reject H0 if |z| > z
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Tests about a Population Mean:
Small-Sample Case (n < 30)
• Test Statistic
σ
Known σ Unknown
x  0
x  0
t
t
/ n
s/ n
This test statistic has a t distribution with n - 1 degrees of
freedom.
• Rejection Rule
One-Tailed
Two-Tailed
H0: μ <μ0 Reject H0 if t > tα
H0: μ> μ0
Reject H0 if t < -tα
H0: μ = μ0
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Reject H0 if |t| > t
A Summary of Forms for Null and
Alternative Hypotheses about a
Population Proportion
• The equality part of the hypotheses always appears in
the null hypothesis.
• In general, a hypothesis test about the value of a
population proportion p must take one of the following
three forms (where p0 is the hypothesized value of the
population proportion).
H0: p > p0
Ha: p < p0
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H0: p < p0
Ha: p > p0
H0: p = p0
Ha: p ≠ p0
Hypothesis Tests About the Difference
Between the Means of Two Populations:
Independent Samples
• Hypotheses
H0: μ1 - μ2 < 0
Ha: μ1 - μ2 > 0
H0: μ1 - μ2 > 0
Ha: μ1 - μ2 < 0
H0: μ1 - μ2 = 0
Ha: μ1 - μ2 ≠ 0
• Test Statistic
Large-Sample
z
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( x1  x2 )  ( 1   2 )
12 n1   22 n2
Small-Sample
t
( x1  x2 )  ( 1   2 )
s2 (1 n1  1 n2 )
Contoh Soal: Specific Motors
• Hypothesis Tests About the Difference Between the
Means of Two Populations: Small-Sample Case
– Rejection Rule
Reject H0 if t > 1.734
(a = .05, d.f. = 18)
– Test Statistic
t
s2 (1 n1  1 n2 )
(n1  1)s12  (n2  1)s22
where: s 
n1  n2  2
2
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( x1  x2 )  ( 1   2 )
Contoh Soal: Express Deliveries
District Office
Seattle
Los Angeles
Boston
Cleveland
New York
Houston
Atlanta
St. Louis
Milwaukee
Denver
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Delivery Time (Hours)
UPX
INTEX
Difference
32
25
7
30
24
6
19
15
4
16
15
1
15
13
2
18
15
3
14
15
-1
10
8
2
7
9
-2
16
11
5
Contoh Soal: Express Deliveries
• Inference About the Difference Between the Means of
Two Populations: Matched Samples
 di ( 7  6... 5)
d 

 2. 7
n
10
2
76.1
 ( di  d )
sd 

 2. 9
n 1
9
d  d
2. 7  0
t

 2. 94
sd n 2. 9 10
– Conclusion
Reject H0.
There is a significant difference between the mean delivery
times for the two services.
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Selamat Belajar
Semoga Sukses
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