03 / CONFIDENCE INTERVALS

Confidence intervals

Use the sample mean to estimate a range of plausible values for the population mean $μ$ .

中文提示：由樣本估計母體平均數嘅範圍。

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One interval. Three key quantities.

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x̄ ± z σ√n

區間 = 樣本平均數 ± 誤差限；E = zσ√n 係半闊度。

Confidence level 95%Sample size n64

4400

Population SD σ12

130

Fixed x̄ = 50. Assume a normal population with known σ. Change the parameters and compare the interval widths.

n = 樣本數；σ = 母體標準差。一次改一個設定，觀察區間點樣變。

KEY RELATIONSHIP

A larger sample gives a narrower interval. A higher confidence level gives a wider interval, with other quantities fixed.

其他條件不變：樣本愈多，區間愈窄；信心水平愈高，區間愈闊。