8.4 Summary of formulas

$(\text{lower value},\text{upper value})=(\text{point estimate}-\text{error bound},\text{point estimate}+\text{error bound})$

$\text{error bound}=\text{upper value}-\text{point estimate}$ OR $\text{error bound}=\frac{\text{upper value}-\text{lower value}}{2}$

Use the Normal Distribution for Means $\text{EBM}=z_{\frac{\alpha }{2}}\cdot \frac{\sigma }{\sqrt{n}}$

The confidence interval has the format $(\overline{x}-\text{EBM},\overline{x}+\text{EBM})$ .

Use the Student's-t Distribution with degrees of freedom $\text{df}=n-1$ . $\text{EBM}=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}$

Use the Normal Distribution for a single population proportion $p\text{'}=\frac{x}{n}$

$\text{EBP}=z_{\frac{\alpha }{2}}\cdot \sqrt{\frac{p\text{'}\cdot q\text{'}}{n}}p\text{'}+q\text{'}=1$

The confidence interval has the format $(p\text{'}-\text{EBP},p\text{'}+\text{EBP})$ .

$\overline{x}$ is a point estimate for $\mu$

$p\text{'}$ is a point estimate for $\rho$

$s$ is a point estimate for $\sigma$