Chapter 7 Formulas and Vocabulary

• Central Limit Theorem for Means (p. 401)
• Mean of the sampling distribution of the sample mean $\overline{x}$, Fact 1 (p. 397). Denoted as ${\mu }_{\overline{x}}=\mu$.
• Sampling distribution of the sample mean $\overline{x}$ (p. 396)
• Sampling distribution of $\overline{x}$ for a normal population, Fact 3 (p. 399)
• Standard error of the mean, Fact 2 (p. 398). Denoted as ${\sigma }_{\overline{x}}=\sigma /\sqrt{n}$.

• Standardizing a normal sampling distribution for means, Fact 4 (p. 399).

  $Z={\displaystyle \frac{\overline{x}-{\mu }_{\overline{x}}}{{\sigma }_{\overline{x}}}}={\displaystyle \frac{\overline{x}-\mu }{\sigma /\sqrt{n}}}$

• Central Limit Theorem for Proportions (p. 418)
• Conditions for approximate normality, Fact 7 (p. 417)
• Mean of the sampling distribution of the sample proportion $\hat{p}$, Fact 5 (p. 416). Denoted as ${\mu }_{\hat{p}}=p$.
• Minimum sample size required (p. 417)
• Sample proportion $\hat{p}$ (p. 415). Denoted as $\hat{p}=X/n$.
• Sampling distribution for any statistic (p. 416)
• Sampling distribution of the sample proportion $\hat{p}$ (p. 416)
• Standard error of the proportion, Fact 6 (p. 416). Denoted as ${\sigma }_{\hat{p}}=\sqrt{pq/n}$

• Standardizing a normal sampling distribution for proportions, Fact 8 (p. 419).

  $Z={\displaystyle \frac{\hat{p}-{\mu }_{\hat{p}}}{{\sigma }_{\hat{p}}}}={\displaystyle \frac{\hat{p}-p}{\sqrt{pq/n}}}$