---
url: "https://questionstar.com/principles-of-survey-research/chapter-4/slide-152.html"
title: "Confidence Interval, Margin of Error, and Sample Size"
type: "lehrbuch-slide"
chapter: 4
chapterTitle: "Sampling"
slide: 152
---

# Confidence Interval, Margin of Error, and Sample Size

*The higher the certainty (confidence probability) we need, the wider the confidence interval becomes — and the larger the margin of error.*

The higher the certainty (confidence probability) we need, the wider the confidence interval becomes — and the larger the margin of error.

1.96

for 95%

→ margin of error ≈ **1 / √n**

2.58

for 99%

→ margin of error ≈ **1.29 / √n**

More certainty → larger z-value → for the same precision you need a larger sample.

95 %

![E = 1.96 · sqrt(0.5(1−0.5)/n) = 1/sqrt(n)](/principles-of-survey-research/media/formel_max_fehler.png)

99 %

![E = 2.58 · sqrt(0.5(1−0.5)/n) = 1.29/sqrt(n)](/principles-of-survey-research/media/formel_e_99.png)

---

*Slide 152 of 274 · Chapter 4: Sampling · Principles of Survey Research · Dr. Paul Marx*