Uji 2 mean
Masalah yang sering dialami dalam penelitian adalah bagaimana
membandingkan dua buah mean dari dua buah sample. Misalkan kita memiliki 2
buah sample. Sampel I dibelajarkan dengan metode A, sedang sample II
dibelajarkan dengan metode B. Setelah mereka mendapatkan perlakuan yang
cukup, kedua sample dites. Bagaimana kita membandingkan dua mean dari skor
tes yang kita peroleh?
Jika sampelnya sample besar, ternyata beda mean X 1  X 2 menyebar
 12  22
menurut distribusi norma dengan mean = 1 – 2 dan standar deviasi
.

n1 n 2
Sehingga table Z bisa kita manfaatkan untuk menguji hipotesis perbedaan 2
mean. Perhatikan bahwa jika 1 dan 2 tidak diketahui maka kita bisa menggunakan s1 dan s2 sebagai penaksirnya. Prosedur pengujian hipotesis dalam hal ini,
sama saja dengan sebelumnya, namun dalam hal ini harga Z adalah:
Z
X1  X 2
s12 s 22

n1 n 2
Example: A doctor wishes to determine which of two diets is more effective in
reducing weight. A sample of 100 obese adults who are interested in
loosing weight is randomly divided into 2 group of 50 people. The mean
weight loss for those who are undergoing diet 1 is 10 pounds with SD =
5 pounds. For diet 2, the average weight loss is 11 pounds with SD = 6
pounds. Do this result indicate a significant difference between the 2
diets at 5% level of significancy?
Answer: H0: 1 = 2
Ha: m 1  m2
X 1  10, s1  5, X 2  11, s 2  6
Z
X1  X 2
s
s

n1 n 2
2
1
2
2
=
10  11
25 / 50  36 / 50

1
1.22
 0.91
Karena harga kritis z untuk  = 5% adalah -1.96 atau 1.96 maka H0
tidak berhasil kita tolak. Jadi tidak ada perbedaan penurunan berat badan
sebagai akibat dari penerapan dua prosedur diet di atas.
Soal-soal
1. Two methods of teaching mathematics, method A and method B, are Compared by administering two similar test to 50 students who have taught by
each method. Method A results show X 1  65, and s1  8 while method B
results show X 2  70 with s 2  10. Do these results indicate thatone method is
more powerful than the other at 5% level of significance?
2. A study is conducted to compare the amount of protein in two brands of
hotdogs. A sample of 100 hotdogs is randomly selected from each brand and
analyzed for their protein contents. Brand A is found to have 18% protein with
SD of 5%, while brand B is found to have 15% protein with SD = 3%. Do
these results indicate that hotdog A significantly contains more protein than
hotdog B at 1% level of significance?
Small sample testing
Diskusi sebelumnya tentang uji beda mean dari dua sample (2 populasi)
mengasumsikan bahwa ukuran sampelnya adalah besar ( 30). Jika salah satu
saja dari sample tersebut berukuran < 30, maka kita berhadapan dengan sample
kecil. Untuk sampel-sampel kecil ini, kembali kita bisa menggunakan t-test untuk
menguji hipotesisnya. Namun pelu diingat, bahwa populasi asal dari sampelsampel ini harus berdistribusi normal.
Jika populasi asal memiliki distribusi normal dengan standar deviasi
sama, maka statistik t memiliki rumus
X1  X 2
t
dimana s =
(n1  1)s12  (n 2  1)s 22
n1  n 2  2
1
1

n1 n 2
Derajat kebebasan dari uji ini adalah n1 + n2 -2.
s
Soal-soal:
1. In comparing the gas mileage of two cars, X and Y, the following
mileage are observed:
Car X
Car Y
28
27.3
27.3 30.2
29
28.2
29.4
27.3
27.5
29.1
28
29.7
28.2
27.8
30.1
28.0
30.5
29.1
29.1
27.5
Are these two cars significantly different in gas consumption based on  = 5% ?
2. A farmer wished to determine which of two stimulants A or B is more effective
in increasing the number of eggs laid by his chickens. He added stimulant A
to the diets of 25 randomly selected chickens and stimulant B to the diets of
another 30 chickens. He observed that for stimulant A the average number of
eggs laid per chickens was 15.3 with SD of 5, while for stimulant B was 17.2
with SD of 4.3. Are this results confirm that stimulant B is better than stimulant
A using  = 5% ?