Sampling Methods Beberapa istilah

  

Sampling Methods

Beberapa istilah

  1. Populasi

  2. Sampel

  3. Parameter

  4. Statistik

  Some of reason for the sampling are :

  

1. To contact the whole population would

be time consuming

  

2. The cost of studying all the items in a

population may be prohibitive

  

3. The physical impossibility of checking

all items in the population.

  4. The destructive nature of some tests

  

Methods to Select a Sample

  

a. Simple random sampling → a sample selected

  so that each item or person in the population has the same chance of being included.

  b. Systematic random sampling → a random

  starting point is selected, and then every kth member of the population is selected.

  c. Stratified random sampling → a population is

  divided into subgroups, called strata, and a sample is randomly selected from each stratum.

  

d. Cluster sampling → a population is divided into

  clusters using naturally occurring geographic Sampel random sederhana memillih sampel dengan metode yang memberikan kesempatan yang sama kepada setiap calon anggota sampel dari anggota populasinya untuk menjadi anggota sampel. Misalnya dalam suatu proses recruiting karyawan baru terdapat 4 orang pelamar yaitu A,B,C, dan D. Dari pelamar ini akan dipilih 2 pelamar untuk mengikuti tes wawancara. Kombinasi yang mungkin sebanyak 2 yang dipilih dari 4 pelamar dengan kesempatan yang sama kepada setiap pelamar adalah pasangan

AB,AC,AD,BC,CD. Karena terdapat 6 pasangan yang

  Sampel sistematis memilih anggota sampel dari suatu populasi dengan interval sama, biasanya diukur dengan ukuran waktu, urutan, ranking atau tempat. Misal kita menginginkan informasi mengenai penghasilan rata-rata pedagang kaki lima dengan menggunakan interval urutan, terlebih dahulu ditentukan urutan yang ke berapa dari anggota populasi yang dipilih menjadi anggota sampel.Misalnya pemilihan menggunakan daftar nama pedagang kaki lima, kemudian akan dipilih secara random dimulai dari urutan kelima sebagai data pertama. Pengambilan anggota sampel

berikutnya diambil pedagang kaki lima pada urutan kelima

  Sampel bertingkat memilih anggota sampel

dengan cara membagi populasi menjadi beberapa

lapisan, disebut strata, secara acak . Misalnya pada suatu penelitian untuk mengetahui minat masyarakat terhadap penggunaan ATM. masyarakat yang akan diteliti dibagi menjadi beberapa lapisan, misalnya pedagang,pegawai negeri, pegawai swasta. Anggota sampel yang digunakan dalam penelitian merupakan penjumlahan dari anggota masyarakat yang

  Sampel berkelompok memilih sampel dengan membuat populasi menjadi beberapa kelompok

misal dalam satu penelitian bertujuan mengetahui

pola perubahan pengeluaran masyarakat di kota Bengkulu . Maka kita bagi kota Bengkulu

  menjadi beberapa lokasi pemilihan sampel, yaitu Kec.Gading Cempaka, Kec. Selebar, Kec. Muara Bangkahulu, Kec Teluk Segara dst. Pada masing- masing kecamatan dipilih beberapa keluarga secara acak untuk

  Sampling Distribution of The Sample Mean

Sample distribution of the sample mean → a probability

distribution of all possible sample means of a given sample size Example :

Tartus industries has seven production employees.The

hourly of each employee are given in table :

  Employee Hourly Earnings Joe $ 7 Sam $ 7 Sue $ 8 Bob $ 8

  The Questions

  a. What is the populations mean?

  

b. What is the sampling distribution of the

sample mean for the samples of size 2?

  c. What the mean of the sampling distributions ?

  d. What the observasions can be made about the population and the sampling distribution?

  The Answer

  a. What is the populations mean? μ = $7 + $7+ $8 +$8 + $7 + $8 + $9 = $7.71

  7

  b. What is the sampling distribution of the sample

  mean for the samples of size 2 ?

  NCn = N! = 7! = 21 n!(N-n)! 2!(7-2)! c. What the mean of the sampling distributions ? μx = Sum of all sample means Total number of samples

d. What the observasions can be made about the

  population and the sampling distribution? Population Values

  40

  30

  20

  40

  30

  20

10 Distribution of sample mean

  10

  

The Central Limit Theorem

Central limit theorem → if all samples of a particular

  size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with large samples.

ESTIMATION AND CONFIDENCE INTERVALS

  Point Estimate → the statistic, computed from

  sample information, which is used to estimate the population parameter.

  Confidence Interval → a range of value

  constructed from sample data so that the population parameter is likely to occur within that range at a specified probability. The specified probability is called the level of confidence.

  Confidence interval for the population mean

  Example : The American Management Assosiation

wishes to have information on the income

of middle managers in the retail idustry.

  

A random sample of 256 managers reveals

a sample mean of $45,420. The standard deviation of this sample is $2,050. The assosiation would like answer to the

  Questions : a.What is the population mean?

b.What is a reasonable range of values for

the population mean? c.What do these results mean?

  The Answers :

a. What is the population mean ?

  in this case, we do not know. We do know the sample mean is $45,420.

  Hence, our best estimate of the unknown population value is the corresponding sample statistic. Thus the sample mean of $45, 420 is a point estimate of the

  

What is a reasonable range of values for the

b. population mean?

  The association decides to use the 95 percent level of confidence. To determine the corresponding confidence interval we use :

  X + z s = $45,420 + 1.96 $ 2,050

   √ n √ 256 = $45,420 + $251

  the usual practice is to round these endpoints to $45,169 and $45,671. these endpoints called the confidence limits. The degree of confidence or the level of confidence is 95 percent and the

c. What do these results mean?

  

Suppose we select many samples of 256

managers, perhaps several hundred. For

each sample,we compute the mean and

the standard deviation and then construct

a 95 percent confidence interval, such as

we did in the previous section. We could expect about 95% of these confidence intervals to contain the population mean.

  About 5% of the intervals would not contain the population mean annual

  A Confidence Interval for Proportion Proportion → the fraction, ratio, or percent

  indicating the part of the sample or the population having a particular trait of interest.

  Sample Proportion : p = x n Confidence Interval for a Population Proportion p + zσ _p

  Confidence Interval for A Population Proportion

  p + z = √ p(1-p)

   n

  Example : The union representing the Bottle Blowers of America (BBA) is considering a proposal to merge with the teamsters union. According to BBA union Bylaws, at least threefourths of the union Membership must approve any merger. A random Sample of 2,000 current BBA members reveals Questions:

What is the estimate of the population proportion ?

Develop a 95 % confidence interval for the

Population proportion. Basing your decision on this

Sample information, can you conclude that the

Necessary of BBA member favor the merger, why?

  Answer : First, calculate the sample proportion from formula p = x = 1,600 = 0,80 n 2,000 Thus, we estimate that 80% of the population favor the merger proposal. The z value corresponding to the 95% level of confidence is 1.96 p + z √ p(1-p) = 0.80 + 1.96√ 0.80(1-0.80) n 2,000 = 0.80 + 0.018 the endpoints of the confidence interval are .782

and .818. the lower endpoint is greater than .75. Hence, we