1. Pertemuan 18 Pengujian Hipotesis Lanjutan
Matakuliah : I0134 – Metoda Statistika
Tahun : 2005
Versi : Revisi
Pertemuan 18 Pengujian Hipotesis Lanjutan

2. Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
Mahasiswa dapat menghasilkan simpulan dari uji hipotesis beda rataan, proporsi dan varians.

3. Uji hipotesis beda rataan Uji hipotesis beda proporsi
Outline Materi
Uji hipotesis beda rataan
Uji hipotesis beda proporsi
Uji hipotesis homogenitas varians

4. 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

5. The matched-sample design can be referred to as blocking.
Inference About the Difference Between the Means of Two Populations: Matched Samples
With a matched-sample design each sampled item provides a pair of data values.
The matched-sample design can be referred to as blocking.
This design often leads to a smaller sampling error than the independent-sample design because variation between sampled items is eliminated as a source of sampling error.

6. Example: Express Deliveries
Inference About the Difference Between the Means of Two Populations: Matched Samples
Let d = the mean of the difference values for the two delivery services for the population of district offices
Hypotheses H0: d = 0, Ha: d 
Rejection Rule
Assuming the population of difference values is approximately normally distributed, the t distribution with n - 1 degrees of freedom applies. With  = .05, t.025 = (9 degrees of freedom).
Reject H0 if t < or if t > 2.262

7. Example: Express Deliveries
Inference About the Difference Between the Means of Two Populations: Matched Samples
Conclusion Reject H0.
There is a significant difference between the mean delivery times for the two services.

8. Hypothesis Tests about p1 - p2
Hypotheses
H0: p1 - p2 < 0
Ha: p1 - p2 > 0
Test statistic
Point Estimator of where p1 = p2
where:

9. Example: MRA Hypothesis Tests about p1 - p2
Can we conclude, using a .05 level of significance, that the proportion of households aware of the client’s product increased after the new advertising campaign?
p1 = proportion of the population of households
“aware” of the product after the new campaign
p2 = proportion of the population of households
“aware” of the product before the new campaign
Hypotheses H0: p1 - p2 < 0
Ha: p1 - p2 > 0

10. Hypothesis Tests about p1 - p2
Example: MRA
Hypothesis Tests about p1 - p2
Rejection Rule Reject H0 if z > 1.645
Test Statistic
Conclusion Do not reject H0.

11. Hypothesis Testing About the Variances of Two Populations
One-Tailed Test
Hypotheses
Test Statistic
Rejection Rule
Reject H0 if F > F where the value of F is based on an F distribution with n1 - 1 (numerator) and n2 - 1 (denominator) d.f.

12. Hypothesis Testing About the Variances of Two Populations
Two-Tailed Test
Hypotheses
Test Statistic
Rejection Rule
Reject H0 if F > F/2 where the value of F/2 is based on an F distribution with n (numerator) and n2 - 1 (denominator) d.f.

13. Example: Buyer’s Digest
Buyer’s Digest has conducted the same test, as was
described earlier, on another 10 thermostats, this time
manufactured by TempKing. The temperature readings
of the ten thermostats are listed below.
We will conduct a hypothesis test with  = .10 to see
if the variances are equal for ThermoRite’s thermostats
and TempKing’s thermostats.
Therm
Temp

14. Example: Buyer’s Digest
Hypothesis Testing About the Variances of Two Populations
Hypotheses
(ThermoRite and TempKing thermo stats have same temperature variance)
(Their variances are not equal)
Rejection Rule
The F distribution table shows that with  = .10,
9 d.f. (numerator), and 9 d.f. (denominator),
F.05 = 3.18.
Reject H0 if F > 3.18

15. Example: Buyer’s Digest
Hypothesis Testing About the Variances of Two Populations
Test Statistic
ThermoRite’s sample variance is .70.
TempKing’s sample variance is 1.52.
F = 1.52/.70 = 2.17
Conclusion
We cannot reject H0. There is insufficient
evidence to conclude that the population
variances differ for the two thermostat brands.

16. Selamat Belajar Semoga Sukses.