T-test (Uji t)

1. Pengertian Uji t

2. Syarat-syarat Uji t

3. KegunaanUji t

4. Penggolongan Uji t

5. Rumus

Pengertian Uji t• Tes t atau Uji t adalah uji statistik yang

digunakan untuk menguji kebenaran atau kepalsuan hipotesis nol .

• Uji t pertama kali dikembangkan oleh William Seely Gosset pada 1915.Awalnya ia menggunakan nama samaran Student, dan huruf t yang terdapat dalam istilah Uji “t “ dari huruf terakhir nama beliau. Uji t disebut juga dengan nama Student t.

2. Persyaratan analisis Uji t

Sampel di ambil secara acak dari populasi berdistribusi normal.

Data berskala interval dan atau rasio.

Kegunaan Uji t Alat analisis data untuk menguji satu

sampel atau dua sampel. Membandingkan dua mean (rata-rata)

untuk menentukan apakah perbedaan rata-rata tersebut perbedaan nyata atau karena kebetulan.

Untuk penggunaan uji t pada satu sampel, dua rata-rata yang di bandingkan adalah mean sampel dan mean populasi.

Penggolongan Uji t

Uji t

Satu Sampel Dua Sampel

Berhubungan (Dependen)

Terpisah(Independen)

Uji t Untuk Satu Sampel

• Rumus

nSx

t

_

sampelbanyak n

sampel deviasi Standard S

populasiMean

sampelMean

tKoefisien _

x

t

Contoh :

1. Seorang peneliti ingin melakukan kajian tentang kemampuan ujian peserta untuk mendapatkan Surat izin Mengemudi (SIM) kendaraan bermotor di Polres . Untuk keperluan penelitian ini di ambil sampel sebanyak 49 peserta, yang dipilih secara acak. Standar kelulusan ujian adalah skor 60 (rata-rata populasi). Dari sampel diperoleh rata-rata skor ujian adalah 55 dengan standar deviasi 15. Berdasarkan data ini , pihak POLRES membuat pernyataan:

“Semua peserta ujian mempunyai kemampuan menyelesaikan soal ujian di bawah standar kelulusan.”

Pertanyaan: Ujilah pernyataan (hipotesis di atas),

60:

60:

1

0

H

HPenyelesaian

.05,0

.33,214,2

5

4915

6055

t

49n

15 S

60

55_

x

Bandingkan hasil perhitungan t di atas dengan tabel t.

db = n -1 = 49-1 = 48ttabel = .679,1)( t

60679,1)( t

Daerah tolak H0 Daerah terima H0

_

x

t > ttabel.

H0 ditolak.

Kesimpulan :Terdapat peserta ujian mempunyai Kemampuan di bawah rata-rata.

-2,23

The management at Massachusetts Savings Bank is always concerned about the quality of service provided to its customers. With the old computer system, a teller at this bank could serve, on average, 22 customers per hour. The management noticed that with this service rate, the waiting time for customers was too long. Recently the management of the bank installed a new computer system in the bank, expecting that it would increase the service rate and consequently make the customers happier by reducing the waiting time.

2.

To check if the new computer system is more efficient than the old system, the management of the bank took a random sample of 18 hours and found that during these hours the mean number of customers served by tellers was 28 per hour with a standard deviation of 2.5. Testing at the 1% significance level, would you conclude that the new computer system is more efficient than the old computer system? Assume that the number of customers served per hour by a teller on this computer system has an approximately normal distribution.

Continu…3.

Grand Auto Corporation produces auto batteries. The company claims that its top-of-the-line Never Die batteries are good, on average, for at least 65 months. A consumer protection agency tested 15 such batteries to check this claim. It found the mean life of these 15 batteries to be 63 months with a standard deviation of 2 months. At the 5% significance level, can you conclude that the claim of this company is true? Assume that the life of such a battery has an approximately normal distribution.

3.

A psychologist claims that the mean age at which children start walking is 12.5 months. Carol wanted to check if this claim is true. She took a random sample of 18 children and found that the mean age at which these children started walking was 12.9 months with a standard deviation of .80 month. Using the 1% significance level, can you conclude that the mean age at which all children start walking is different from 12.5 months? Assume that the ages at which all children start walking have an approximately normal distribution.

4.

5. Terdapat asumsi bahwa dari suatu populasi mahasiswa Sistem Informasi semester 5 rata-rata nilai statistika 2 adalah 60, untuk menguji asumsi tersebut diambil sampel sebanyak 10 mahasiswa, Ujilah apakah asumsi tersebut apakah terdapat perbedaan yang signifikan antara rata –rata sampel dengan rata-rata populasi. Gunakan taraf signifikan alpha 0.05

X 80 90 60 60 90 60 80 50 70 60

Penyelesaian

• s = 14,142• • t =2,236

• ttabel=2.262

• t < ttabel

• H0 diterima. So, tidak ada perbedaan yang signifikan antara rata –rata sampel dengan rata-rata populasi.

7

x

Output SPSS

One-Sample Statistics

10 7,00 1,41 ,45Nilai stat2N Mean Std. Deviation

Std. ErrorMean

One-Sample Test

2,236 9 ,052 1,00 -1,17E-02 2,01Nilai stat2t df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value = 6