2. PENGUJIAN HIPOTESIS 1 Pertemuan 9
Matakuliah : I STATISTIK PROBABILITAS
Tahun : 2009
PENGUJIAN HIPOTESIS 1 Pertemuan 9

3. Uji hipotesis nilai tengah Uji hipotesis beda dua nilai tengah
Materi
Uji hipotesis nilai tengah
Uji hipotesis beda dua nilai tengah
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4. 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:
Tests About a Population Mean:
Small-Sample Case
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5. 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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6. 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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7. 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  must take one of the following three forms (where 0 is the hypothesized value of the population mean).
H0:  >  H0:  <  H0:  = 0
Ha:  <  Ha:  >  Ha:  ≠ 0
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8. Type I and Type II Errors Contoh Soal: Metro EMS
Population Condition
H0 True Ha True
Conclusion ( ) ( )
Accept H Correct Type II
(Conclude  Conclusion Error
Reject H Type I Correct
(Conclude  rror Conclusion
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9. The Steps of Hypothesis Testing
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.
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10. One-Tailed Tests about a Population Mean: Large-Sample Case (n > 30)
Hypotheses
H0:   or H0: 
Ha: Ha:
Test Statistic  Known  Unknown
Rejection Rule
Reject H0 if z > zReject H0 if z < -z
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11. Two-Tailed Tests about a Population Mean: Large-Sample Case (n > 30)
Hypotheses H0: = 
Ha: 
Test Statistic  Known  Unknown
Rejection Rule
Reject H0 if |z| > z
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12. Example: One Tail Test H0: m £ 368 H1: m > 368
Q. Does an average box of cereal contain more than 368 grams of cereal? A random sample of 25 boxes showed = The company has specified s to be 15 grams. Test at the a = level.
368 gm.
H0: m £ H1: m > 368
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13. Finding Critical Value: One Tail
What is Z given a = 0.05?
Standardized Cumulative Normal Distribution Table (Portion)
.05 Z
.04
.06
1.6
.9495
.9505
.9515
.95
a = .05
1.7
.9591
.9599
.9608
1.8
.9671
.9678
.9686
1.645 Z
Critical Value = 1.645
1.9
.9738
.9744
.9750
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14. Example Solution: One Tail Test
H0: m £ H1: m > 368
Test Statistic:
Decision:
Conclusion:
a = 0.5
n = 25
Critical Value: 1.645
Reject
Do Not Reject at a = .05
.05
No evidence that true mean is more than 368
1.645 Z
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1.50

15. p -Value Solution p-Value is P(Z ³ 1.50) = 0.0668 Z 1.50
Use the alternative hypothesis to find the direction of the rejection region.
P-Value =.0668 Z
1.50
From Z Table: Lookup 1.50 to Obtain .9332
Z Value of Sample Statistic
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16. (p-Value = 0.0668) ³ (a = 0.05) Do Not Reject.
p -Value Solution
(continued)
(p-Value = ) ³ (a = 0.05) Do Not Reject.
p Value =
Reject
a = 0.05 Z
1.645
1.50
Test Statistic 1.50 is in the Do Not Reject Region
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17. Example: Two-Tail Test
Q. Does an average box of cereal contain 368 grams of cereal? A random sample of 25 boxes showed = The company has specified s to be 15 grams. Test at the a = level.
368 gm.
H0: m = H1: m ¹ 368
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18. Example Solution: Two-Tail Test
H0: m = H1: m ¹ 368
Test Statistic:
Decision:
Conclusion:
a = 0.05
n = 25
Critical Value: ±1.96
Reject
Do Not Reject at a = .05
.025
.025
No Evidence that True Mean is Not 368
-1.96
1.96 Z
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1.50

19. (p Value = 0.1336) ³ (a = 0.05) Do Not Reject.
p-Value Solution
(p Value = ) ³ (a = 0.05) Do Not Reject.
p Value = 2 x
Reject
Reject
Test Statistic 1.50 is in the Do Not Reject Region
a = 0.05 Z
1.50
1.96
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20. Tests about a Population Mean: Small-Sample Case (n < 30)
Test Statistic  Known  Unknown
This test statistic has a t distribution with n - 1 degrees of freedom.
Rejection Rule
One-Tailed Two-Tailed
Ha:  Reject H0 if t > t
Ha:  Reject H0 if t < -t
Ha:   Reject H0 if |t| > t
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21. Example: One-Tail t Test
Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed X = 372.5, and s = 15. Test at the a = level.
368 gm.
H0: m £ H1: m > 368
s is not given
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22. Example Solution: One-Tail
H0: m £ H1: m > 368
Test Statistic:
Decision:
Conclusion:
a = 0.01
n = 36, df = 35
Critical Value:
Reject
Do Not Reject at a = .01
.01
No evidence that true mean is more than 368
2.4377
t35
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1.80

23. (p Value is between .025 and .05) ³ (a = 0.01). Do Not Reject.
p -Value Solution
(p Value is between .025 and .05) ³ (a = 0.01). Do Not Reject.
p Value = [.025, .05]
Reject
a = 0.01
t35
1.80
2.4377
Test Statistic 1.80 is in the Do Not Reject Region
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24. Hypothesis Tests About the Difference Between the Means of Two Populations: Independent Samples
Hypotheses
H0: 1 - 2 < H0: 1 - 2 > H0: 1 - 2 = 0
Ha: 1 - 2 > Ha: 1 - 2 < Ha: 1 - 2  0
Test Statistic
Large-Sample Small-Sample
where,
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25. Critical Value untuk statistik uji z: Ha wilayah kritik (tolak H0)
1 - 2 > d0 z > z
1 - 2 < d0 z < -z
1 - 2  d0
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26. Critical Value untuk statistik uji t: Ha wilayah kritik
1 - 2 > d0 t > t
1 - 2 < d0 t < -t
1 - 2  d0
v = n1 – n derajat bebas
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27. 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 = 0.05, d.f. = 18)
Test Statistic
where:
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