---
url: "https://questionstar.com/principles-of-survey-research/chapter-5/slide-198.html"
title: "Hypothesis Testing"
type: "lehrbuch-slide"
chapter: 5
chapterTitle: "Data Analysis: A Concise Overview of Statistical Techniques"
slide: 198
---

# Hypothesis Testing

*Step 4 · Comparison*

Step 4 · Formulating the decision rule

Critical values of χ² for various significance levels α

| df | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 |
|------|------|------|------|------|------|------|------|------|
| 1 | — | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 |
| 2 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 |
| 3 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345 |
| 4 | 0.297 | 0.484 | 0.711 | 1.064 | 7.779 | 9.488 | 11.143 | 13.277 |
| 5 | 0.554 | 0.831 | 1.145 | 1.610 | 9.236 | 11.071 | 12.833 | 15.086 |
| 6 | 0.872 | 1.237 | 1.635 | 2.204 | 10.645 | 12.592 | 14.449 | 16.812 |
| 7 | 1.239 | 1.690 | 2.167 | 2.833 | 12.017 | 14.067 | 16.013 | 18.475 |
| 8 | 1.646 | 2.180 | 2.733 | 3.490 | 13.362 | 15.507 | 17.535 | 20.090 |
| 9 | 2.088 | 2.700 | 3.325 | 4.168 | 14.684 | 16.919 | 19.023 | 21.666 |
| 10 | 2.558 | 3.247 | 3.940 | 4.865 | 15.987 | 18.307 | 20.483 | 23.209 |

df = (r−1)(c−1)

df — degrees of freedom

r — number of rows

c — number of columns

df = (2−1)(2−1) = 1

If the probability of TScal < (α) , then reject H₀ .

or

If TScal > TScr , then reject H₀ .

χ ² ~cal = 3.333

χ ² ~cr = 3.841

3.333 < 3.841 ⟹ χ ² ~cal < χ ² ~cr

H₀ CANNOT be rejected

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*Slide 198 of 274 · Chapter 5: Data Analysis: A Concise Overview of Statistical Techniques · Principles of Survey Research · Dr. Paul Marx*