Sampling Methods
Beberapa istilah
1. Populasi
2. Sampel
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.
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 or other boundaries. Then, clusters are
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
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
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 :
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?
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
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 (n > 30) = X + z s
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.
Questions :
a.What is the population mean?
b.What is a reasonable range of values for
the population mean?
The Answers :
a. What is the population mean ?
b.
What is a reasonable range of values for the 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
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
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 + zσp
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
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
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
