Estimation - Theory & Concepts

Point estimation, confidence intervals for means, proportions, and variances, and prediction/tolerance intervals.

Confidence Interval & Parameter Estimation

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95% Confidence Interval

z_{\alpha/2} = z_{0.025} = 1.96

[2416.84, 2583.16]

\bar{x} \pm E = 2500.0 \pm 83.16

(Margin of Error)

Interpretation: We are 95% confident that the true population mean lies between 2416.84 and 2583.16. Increasing sample size (

n

) reduces the standard error, making the interval narrower.

Sample Mean (

\bar{x}

)2500

Standard Deviation (

s

)300

Sample Size (

n

)50

Standard Error: $\sigma_{\bar{x}} = s / \sqrt{n} = 42.426$

Confidence Level (

1 - \alpha

)

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