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

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

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

Hypothesis Tests About the Difference Between the Means of Two Populations: Independent Samples Hypotheses H0: 1 - 2 < 0 H0: 1 - 2 > 0 H0: 1 - 2 = 0 Ha: 1 - 2 > 0 Ha: 1 - 2 < 0 Ha: 1 - 2  0 Test Statistic Large-Sample Small-Sample

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.

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 = 2.262 (9 degrees of freedom). Reject H0 if t < -2.262 or if t > 2.262

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.

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

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

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.

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.

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 n1 - 1 (numerator) and n2 - 1 (denominator) d.f.

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. 1 2 3 4 5 6 7 8 9 10 Temp. 66.4 67.8 68.2 70.3 69.5 68.0 68.1 68.6 67.9 66.2

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

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.

Selamat Belajar Semoga Sukses.