数学

Confidence Interval Calculator

Sample Mean (x̄)

Std Deviation (σ or s)

サンプルサイズ（n）

Confidence Level

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とは何か Confidence Interval Calculator?

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A confidence interval (CI) gives a range within which the true population parameter falls with a specified probability. A 95% CI means: if the experiment were repeated many times, 95% of CIs would contain the true value.

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公式

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f(x)CI = x̄ ± z × (σ/√n), where z=1.96 for 95% CI, z=2.576 for 99% CI

変数の説明

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記号	名前	単位	説明
x̄	Sample mean	value	—
σ	Standard deviation	value	—
n	Sample size	count	—
z	Z-score	standard deviations	—

方法 Confidence Interval Calculator

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1CI = x̄ ± z × (σ/√n)
2z = 1.96 for 95% CI; 2.576 for 99% CI
3Width depends on sample size n and standard deviation σ
4Larger sample → narrower interval → more precise estimate

解いた例

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例 1

入力:Mean 50, SD 10, n=100, 95% CI

結果:CI = 50 ± 1.96×(10/√100) = 50 ± 1.96 = [48.04, 51.96]

実際の応用

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Medical research and clinical trials

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Quality control in manufacturing

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Public opinion polling

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A/B testing in web design

Common Confidence Levels

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Confidence level	z value	Interpretation
90%	1.645	Wide interval, less certain
95%	1.960	Standard in most research
99%	2.576	Narrow claims need this
99.9%	3.291	Used for safety-critical decisions

よくある質問

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What does a 95% confidence interval mean?

If repeated many times, 95% of intervals would contain the true population parameter. Not 95% chance this specific interval does.

When should I use 99% vs 95% CI?

99% is more conservative (wider). Use when high certainty needed (medical, safety). 95% standard in most research.

How does sample size affect confidence intervals?

Larger samples narrow the interval (more precision). √n in denominator means doubling n tightens by √2.

Regional Guides

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Academic/Medical▾

95% CI standard; 99% for stricter contexts

Industrial QC▾

95% typical; 99.7% for critical processes

Survey research▾

95% CI with margin of error reporting

参考文献

›Confidence intervals — Khan Academy

Confidence Interval Calculator