Pertemuan 8

Apakah yang dimaksud dengan hipotesis?

Kenapa kita menggunakan pengujian hipotesis?

Definisi

●Hipotesis: A statement about a population parameter

●Uji hipotesis digunakan karena kita menggunakan

sampel.

Apa tahap2 pengujian hipotesis?

Tahap Pengujian Hipotesis

2

Select sig. level

3

Identify test

statistic

1

State null &

alt. hypothesis

4

Formulate

Decision

RuleDecision

Apakah hipotesis nol dan alternatif?

Bagaimana menentukan hipotesis nol dan alternatif?

Hipotesis

●Null hypothesis (hipotesis nol): hipotesis tentang

populasi

●Alternate hypothesis (hipotesis alternatif): hipotesis

yang diterima saat hipotesis nol ditolak

Cara menentukan Ho

●Yang ingin dibuktikan = hipotesis alternatif

●A company that makes processed cheese is interested in

determining whether some suppliers that provide milk for the

processing operation are adding water to their milk to increase

the amount supplied to the processing operation. It is known

that excess water reduces the freezing point of the milk. The

freezing point of natural milk is normally distributed, with a

mean of -0.545 Celsius. The cheese company is only interested

in determining whether the freezing point of the milk is less

than what would be expected from natural milk.

Cara Menentukan Ho

●whether the freezing point of the milk is less than

what would be expected from natural milk

●Rata2 susu biasa: -0.545 Celsius

●Fokus pengujian = less than natural milk = < -0.545 C.

●Ha: rata2 < -0.545 C

●H0: rata2 >= -0.545 C

Apakah yang dimaksud dengan tingkat signifikansi?

Berapa tingkat signifikansi yang digunakan di dalam

ilmu sosial?

Tingkat Signifikansi

●Adalah: kemungkinan menolak H0, padahal H0 adalah

yang benar

–α = 1-tingkat keyakinan

●5% = consumer research

●1% = quality assurance

●10% = political polling

Apa hubungan tingkat signifikansi dan type 1 error?

Apa perbedaan type 1 and type 2 error?

Type 1 and Type 2 Error

H0 diterima H0 ditolak

H0 benar Keputusan

benar

Type 1

H0 salah Type 2 Keputusan

benar

Rumus 1 Sample Test

𝑍 = 𝑋 − μ

σ 𝑛𝑍 =

𝑋 − μ

𝑠 𝑛𝑡 =

𝑋 − μ

𝑠 𝑛

Z = nilai normal standar

t = nilai distribusi t

Xbar = rata2 sampel

μ = rata2 populasi

σ = stdev populasi

s = stdev sampel

n = jumlah sampel

Kapan menggunakan Z atau t?

N >= 30?

σ diketahui?

𝑍 = 𝑋 − μ

σ 𝑛𝑍 =

𝑋 − μ

𝑠 𝑛

𝑡 = 𝑋 − μ

𝑠 𝑛

TIDAK

TIDAKYa

Ya

Kapan pakai 1 tailed dan 2 tailed test?

1 tailed atau 2 tailed?

●an economist wishes to determine whether there is

evidence that mean family income in a community

exceeds $50,000

●an economist wishes to determine whether there is

evidence that mean family income in a community

equals $50,000

Latihan

●How many tissues should the Kimberly Clark

Corporation package of Kleenex contain? Researchers

determined that 60 tissues is the mean number of

tissues used during a cold. Suppose a random sample

of 100 Kleenex users yielded the following data on the

number of tissues used during a cold: Xbar = 52, S =

22.

●Give the null and alternative hypotheses.

●Using the sample information provided, calculate the

value of the test statistic.

Latihan

●The owner of a local nightclub has recently surveyed a

random sample of n = 250 customers of the club. She

would now like to determine whether or not the mean

age of her customers is over 30. If so, she plans to alter

the entertainment to appeal to an older crowd. If not,

no entertainment changes will be made. Suppose she

found that the sample mean was 30.45 years and the

sample standard deviation was 5 years. If she wants to

be 99% confident in her decision, what decision should

she make?

Latihan

●An entrepreneur is considering the purchase of a coin-

operated laundry. The current owner claims that over

the past 5 years, the mean daily revenue was $675 with

a standard deviation of $75. A sample of 30 days

reveals a daily mean revenue of $625. If you were to

test the null hypothesis that the daily mean revenue was

$675 and decide not to reject the null hypothesis, what

can you conclude?

Rumus Proporsi

𝑍 =𝑝 − π

π 1 − π 𝑛

Z = nilai normal standar

n = jumlah sampel

p = proporsi sampel

π = proporsi populasi

Latihan

●To test this claim against the alternative that the actual

proportion of doctors who recommend aspirin is less

than 0.90, a random sample of 100 doctors results in 83

who indicate that they recommend aspirin.