7.5: Chapter Formula Review

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7.1 The Central Limit Theorem for Sample Means

The Central Limit Theorem for Sample Means:

\(\overline{X} \sim N\left(\mu_{\overline{x}}, \frac{\sigma}{\sqrt{n}}\right)\)

\(Z=\frac{\overline{X}-\mu_{\overline{X}}}{\sigma_{X}}=\frac{\overline{X}-\mu}{\sigma / \sqrt{n}}\)

The Mean \(\overline{X} : \mu_{\overline x}\)

Central Limit Theorem for Sample Means z-score \(z=\frac{\overline{x}-\mu_{\overline{x}}}{\left(\frac{\sigma}{\sqrt{n}}\right)}\)

Standard Error of the Mean (Standard Deviation \((\overline{X}) ) : \frac{\sigma}{\sqrt{n}}\)

Finite Population Correction Factor for the sampling distribution of means: \(Z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}} \cdot \sqrt{\frac{N-n}{N-1}}}\)

Finite Population Correction Factor for the sampling distribution of proportions: \(\sigma_{\mathrm{p}^{\prime}}=\sqrt{\frac{p(1-p)}{n}} \times \sqrt{\frac{N-n}{N-1}}\)