Unit 3 Formula Sheet
Chapter 5
Standard Score or z-Score:
\(z=\frac{ \text {Value}- \text {Mean} }{ \text {Standard Deviation} }=\frac{x-\mu}\sigma\)
Transforming a z-Score to an x-Value:
\(x=\mu+z \cdot \sigma\)
Central Limit Theorem:
(\(n\geq30\) or population is normally distributed)
Mean of the Sampling Distribution: \(\mu_x=\mu\)
Standard Deviation of the Sampling Distribution (Standard Error):
\(\sigma_x=\frac\sigma{\sqrt n}\)
z-Score \(=\frac{{\displaystyle\overset\_x}-\mu_x}{\sigma_x}=\frac{\displaystyle\overset\_x-\mu}{ \frac {\sigma}{\sqrt n}}\)
Chapter 6
Confidence Interval for the Mean:
\(\overset-x-E<\mu<\overset-x+E\)
\(E=t_c\frac s{\sqrt n}\)
Minimum Sample Size to Estimate the Mean:
\(n=\left(\frac{z_c\sigma}E\right)^2\)
Population Proportion:
\(\widehat p=\frac xn\)
Confidence Interval for Population Proportion:
\(\widehat p-E\;<\;p\;<\;\widehat p+E\)
\(E=z_c\sqrt{\frac{\displaystyle\widehat p\widehat q}n}\)
Minimum Sample Size to Estimate:
\(n=\widehat p\widehat q\left(\frac{z_c}E\right)^2\)