Lesson 5.4: Confidence Intervals
Confidence Interval (CI) is a range of values used to estimate a population parameter (like mean or proportion) with a certain level of confidence.
🔹 Key Concepts
1️⃣ Definition
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A confidence interval tells us how sure we are about our estimate.
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Example: The average height of students is 165 cm ± 3 cm (95% CI).
→ Means we are 95% confident that the true average height lies between 162 cm and 168 cm.
2️⃣ Confidence Level
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Common levels: 90%, 95%, 99%.
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95% CI means: If we repeat the experiment 100 times, in about 95 times the true value will fall inside the interval.
3️⃣ Formula (for Mean, large sample)
CI=xˉ±Z×σnCI = \bar{x} \pm Z \times \frac{\sigma}{\sqrt{n}}
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xˉ\bar{x} = sample mean
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ZZ = Z-score (1.96 for 95% CI)
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σ\sigma = standard deviation
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nn = sample size
✅ Quick Recap:
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CI gives a range of possible values.
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Wider interval = more uncertainty.
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Narrow interval = more precise estimate.
