Pendugaan Parameter (II) Pertemuan 10 Matakuliah : I0014 / Biostatistika Tahun : 2008 Pendugaan Parameter (II) Pertemuan 10

Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat menghitung pendugaan nilai tengah populasi (C3) Mahasiswa dapat menghitung pendugaan ragam populasi (C3) Mahasiswa dapat menghitung pendugaan proporsi populasi (C3) Bina Nusantara

Outline Materi Pendugaan Nilai tengah Pendugaan Ragam Pendugaan Proporsi Bina Nusantara

Jenis Penduga Point Estimate A single-valued estimate. A single element chosen from a sampling distribution. Conveys little information about the actual value of the population parameter, about the accuracy of the estimate. Confidence Interval or Interval Estimate An interval or range of values believed to include the unknown population parameter. Associated with the interval is a measure of the confidence we have that the interval does indeed contain the parameter of interest. Bina Nusantara

Selang Kepercayaan (1-a )100% We define as the z value that cuts off a right-tail area of under the standard normal curve. (1-) is called the confidence coefficient.  is called the error probability, and (1-)100% is called the confidence level. 5 4 3 2 1 - . Z f ( z ) S t a n d r N o m l D i s b u z n ± a s 2 (1 - )100% Conf idence Int erval: x Bina Nusantara

Selang Kepercayaan untuk  bila  Tidak Diketahui A (1-)100% confidence interval for  when  is not known (assuming a normally distributed population): where is the value of the t distribution with n-1 degrees of freedom that cuts off a tail area of to its right. Bina Nusantara

Penduga Selang untuk Proporsi Bina Nusantara

Selang Kepercayaan untuk Ragam A (1-)100% confidence interval for the population variance * (where the population is assumed normal): where is the value of the chi-square distribution with n-1 degrees of freedom that cuts off an area to its right and is the value of the distribution that cuts off an area of to its left (equivalently, an area of to its right). * Note: Because the chi-square distribution is skewed, the confidence interval for the population variance is not symmetric Bina Nusantara

Selang Kepercayaan untuk Beda Dua Mean Populasi A large-sample (1-)100% confidence interval for the difference between two population means, 1- 2 , using independent random samples: Bina Nusantara

When sample sizes are small (n1< 30 or n2< 30 or both), and both populations are normally distributed, the test statistic has approximately a t distribution with degrees of freedom given by (round downward to the nearest integer if necessary): Bina Nusantara

Pendugaan Ragam Gabungan A pooled estimate of the common population variance, based on a sample variance s12 from a sample of size n1 and a sample variance s22 from a sample of size n2 is given by: The degrees of freedom associated with this estimator is: df = (n1+ n2-2) The pooled estimate of the variance is a weighted average of the two individual sample variances, with weights proportional to the sizes of the two samples. That is, larger weight is given to the variance from the larger sample. Bina Nusantara

Selang Kepercayaan menggunakan Ragam Gabungan A (1-) 100% confidence interval for the difference between two population means, 1- 2 , using independent random samples and assuming equal population variances: Bina Nusantara

Selang Kepercayaan Beda Dua Proporsi A (1-) 100% large-sample confidence interval for the difference between two population proportions: Bina Nusantara

Selang kepercayaan Rasio Dua Ragam Bina Nusantara

Penutup Sampai saat ini Anda telah mempelajari pendugaan titik dan selang, baik untuk satu populasi maupun dua populasi Untuk dapat lebih memahami penggunaan pendugaan tersebut, cobalah Anda pelajari materi penunjang, dan mengerjakan latihan Bina Nusantara