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MenengahAplikasi·11 min

Membangun Interval Kepercayaan dengan Simpangan Baku

Pelajari cara membangun interval kepercayaan menggunakan simpangan baku. Pahami arti tingkat kepercayaan dan cara menginterpretasi CI dalam skenario dunia nyata.

Apa itu Interval Kepercayaan?

Interval kepercayaan (CI) adalah rentang nilai yang kemungkinan mengandung parameter populasi sebenarnya. Alih-alih memberikan satu estimasi titik, CI mengakui ketidakpastian dengan menyediakan suatu rentang.

“Kita 95% yakin rata-rata sebenarnya berada antara 48,2 dan 51,8”

95% CI: [48.2, 51.8]

Rumus

Interval kepercayaan untuk rata-rata populasi adalah:

Rumus Interval Kepercayaan

CI = x̄ ± z* × (σ / √n)
  • x̄ = rata-rata sampel
  • z* = nilai kritis (1,96 untuk 95% CI)
  • σ = simpangan baku
  • n = ukuran sampel
  • σ/√n = galat baku
Tingkat KepercayaanNilai z*
90%1,645
95%1,960
99%2,576

Interpretasi yang Benar

Kesalahpahaman Umum

CI 95% TIDAK berarti “ada probabilitas 95% bahwa rata-rata sebenarnya berada dalam interval ini.” Rata-rata sebenarnya berada atau tidak berada dalam interval—nilainya tetap.

Interpretasi yang Benar

“Jika kita mengulangi proses pengambilan sampel ini berkali-kali, 95% dari interval yang dihitung akan mengandung rata-rata populasi sebenarnya.”

Contoh Perhitungan

Contoh: Kepuasan Pelanggan

Anda mensurvei 100 pelanggan dan mendapati skor kepuasan rata-rata 7,5 dengan simpangan baku 1,5. Hitung CI 95%.
1

Cari galat baku

SE = 1,5 / √100 = 0,15
2

Hitung margin kesalahan

ME = 1,96 × 0,15 = 0,294
3

Bangun interval

CI = 7,5 ± 0,294 = [7,21; 7,79]

Interpretasi: Kita 95% yakin bahwa rata-rata kepuasan pelanggan sebenarnya berada antara 7,21 dan 7,79.

Apa yang Mempengaruhi Lebar CI?

Ukuran Sampel (n)

n lebih besar = CI lebih sempit Lebih banyak data = lebih presisi

Simpangan Baku (σ)

σ lebih besar = CI lebih lebar Lebih banyak variabilitas = kurang pasti

Tingkat Kepercayaan

Kepercayaan lebih tinggi = CI lebih lebar CI 99% lebih lebar dari CI 95%

Further Reading

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How to Read This Article

A statistics tutorial is a practical interpretation guide, not just a formula dump. It refers to the assumptions, notation, and reporting language that analysts need when they explain a result to a teacher, manager, client, or reviewer. The article body covers the specific topic, while the sections below create a common interpretation frame that readers can reuse across related metrics.

Reading goalWhat to focus onCommon mistake
DefinitionWhat the metric is and what quantity it summarizesTreating the formula as self-explanatory
Formula choiceSample versus population assumptions and notationUsing n when n-1 is required or vice versa
InterpretationWhether the result indicates concentration, spread, or riskCalling a large value good or bad without context

Frequently Asked Questions

How should I interpret a high standard deviation?

A high standard deviation means the observations are spread farther from the mean on average. Whether that spread is acceptable depends on the context: wide dispersion might signal risk in finance, instability in manufacturing, or genuine natural variation in scientific data.

Why do some articles mention n while others mention n-1?

The denominator reflects the difference between population and sample formulas. Population variance and population standard deviation use N because the full dataset is known. Sample variance and sample standard deviation often use n-1 because Bessel’s correction reduces bias when estimating population spread from a sample.

What is a statistical interpretation guide?

A statistical interpretation guide is a page that moves beyond arithmetic and explains meaning. It tells you what a metric is, when the formula applies, and how to describe the result in plain English without overstating certainty.

Can I cite this article in a report?

You should cite the underlying authoritative reference for formal work whenever possible. This page is best used as an explanatory bridge that helps you understand the concept before quoting the original standard or handbook.

Why include direct citations on every article page?

Direct citations give readers a route to verify the definition, notation, and assumptions. That improves trust and reduces the chance that a simplified explanation is mistaken for the entire technical standard.

Authoritative References

These sources define the concepts referenced most often across our articles. Bessel's correction is a sample adjustment, variance is a squared measure of spread, and standard deviation is the square root of variance expressed in the same units as the data.