Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Selected Formulas

Chapter 2

$Relative Frequency = (frequency) / n$ $Relative Frequency = (frequency) / n$

$\bar{x} = \frac{Σ x}{n}$ $\bar{x} = \frac{Σ x}{n}$

$s^{2} = \frac{Σ {(x - \bar{x})}^{2}}{n - 1} = \frac{Σ x^{2} - \frac{{(Σ x)}^{2}}{n}}{n - 1}$ $s^{2} = \frac{Σ {(x - \bar{x})}^{2}}{n - 1} = \frac{Σ x^{2} - \frac{{(Σ x)}^{2}}{n}}{n - 1}$

$s = \sqrt{s^{2}}$ $s = \sqrt{s^{2}}$

$z = \frac{x - μ}{σ} = \frac{x - \bar{x}}{s}$ $z = \frac{x - μ}{σ} = \frac{x - \bar{x}}{s}$

$Chebyshev = At least (1 - \frac{1}{k^{2}}) 100 %$ $Chebyshev = At least (1 - \frac{1}{k^{2}}) 100 %$

$IQR = Q_{U} - Q_{L}$ $IQR = Q_{U} - Q_{L}$

Chapter 3

$P (A^{c}) = 1 - P (A)$ $P (A^{c}) = 1 - P (A)$

$\begin{array}{r} P (A \cup B) & = & P (A) + P (B) - P (A \cap B) \\ = & P (A) + P (B) if A and B mutually exclusive \end{array}$ $\begin{array}{r} P (A \cup B) & = & P (A) + P (B) - P (A \cap B) \\ = & P (A) + P (B) if A and B mutually exclusive \end{array}$

$\begin{array}{r} P (A \cap B) & = & P (A | B) \cdot P (B) = P (B | A) \cdot P (A) \\ = & P (A) \cdot P (B) if A and B independent \end{array}$ $\begin{array}{r} P (A \cap B) & = & P (A | B) \cdot P (B) = P (B | A) \cdot P (A) \\ = & P (A) \cdot P (B) if A and B independent \end{array}$

$P (A | B) = \frac{P (A \cap B)}{P (B)}$ $P (A | B) = \frac{P (A \cap B)}{P (B)}$

$(\begin{matrix} N \\ n \end{matrix}) = \frac{N!}{n! (N - n)!}$ $(\begin{matrix} N \\ n \end{matrix}) = \frac{N!}{n! (N - n)!}$

Chapter 4

Key Formulas
Random Variable	Prob. Dist’n	Mean	Variance
General Discrete:	Table, formula, or graph for p(`x`)	$\sum_{all x} x \cdot p (x)$ $\sum_{all x} x \cdot p (x)$	$\sum_{all x} {(x - μ)}^{2} \cdot p (x)$ $\sum_{all x} {(x - μ)}^{2} \cdot p (x)$
*Binomial:*	$p (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x}$ $p (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x}$ $x = 0, 1, 2, . . ., n$ $x = 0, 1, 2, . . ., n$	$n p$ $n p$	$n p q$ $n p q$
*Normal:*	$f (x) = \frac{1}{σ \sqrt{2 π}} e^{- \frac{1}{2} {[(x - μ) / σ]}^{2}}$ $f (x) = \frac{1}{σ \sqrt{2 π}} e^{- \frac{1}{2} {[(x - μ) / σ]}^{2}}$	$μ$ $μ$	$σ^{2}$ $σ^{2}$
*Standard Normal:*	$f (z) = \frac{1}{\sqrt{2 π}} e^{- \frac{1}{2} {(z)}^{2}}$ $f (z) = \frac{1}{\sqrt{2 π}} e^{- \frac{1}{2} {(z)}^{2}}$ $z = (x - μ) / σ$ $z = (x - μ) / σ$	$μ = 0$ $μ = 0$	$σ^{2} = 1$ $σ^{2} = 1$
*Sample Mean: (large n)*	$f (\bar{x}) = \frac{1}{σ_{\bar{x}} \sqrt{2 π}} e^{- \frac{1}{2} {[(\bar{x} - μ) / σ_{\bar{x}}]}^{2}}$ $f (\bar{x}) = \frac{1}{σ_{\bar{x}} \sqrt{2 π}} e^{- \frac{1}{2} {[(\bar{x} - μ) / σ_{\bar{x}}]}^{2}}$	$μ_{\bar{x}} = μ$ $μ_{\bar{x}} = μ$	$σ_{\bar{x}} 2 = σ^{2} / n$ $σ_{\bar{x}} 2 = σ^{2} / n$

Chapter 5

$\begin{array}{r} CI for μ : \bar{x} & \pm & (z_{α / 2}) σ / \sqrt{n} (large n) \\ \bar{x} & \pm & (t_{α / 2}) s / \sqrt{n} (small n, σ unknown) \end{array}$ $\begin{array}{r} CI for μ : \bar{x} & \pm & (z_{α / 2}) σ / \sqrt{n} (large n) \\ \bar{x} & \pm & (t_{α / 2}) s / \sqrt{n} (small n, σ unknown) \end{array}$

$CI for p : \hat{p} \pm z_{α / 2} \sqrt{\frac{\hat{p} \hat{q}}{n}}$ $CI for p : \hat{p} \pm z_{α / 2} \sqrt{\frac{\hat{p} \hat{q}}{n}}$

$\begin{array}{r} Estimating μ : n & = & {(z_{α / 2})}^{2} (σ^{2}) / {(SE)}^{2} \\ Estimating p : n & = & {(z_{α / 2})}^{2} (p q) / {(SE)}^{2} \end{array}$ $\begin{array}{r} Estimating μ : n & = & {(z_{α / 2})}^{2} (σ^{2}) / {(SE)}^{2} \\ Estimating p : n & = & {(z_{α / 2})}^{2} (p q) / {(SE)}^{2} \end{array}$

Chapter 6

$Test for μ : z = \frac{\bar{x} - μ}{σ / \sqrt{n}} (large n)$ $Test for μ : z = \frac{\bar{x} - μ}{σ / \sqrt{n}} (large n)$

$t = \frac{\bar{x} - μ}{s / \sqrt{n}} (small n, σ unknown)$ $t = \frac{\bar{x} - μ}{s / \sqrt{n}} (small n, σ unknown)$

$Test for p : z = \frac{\hat{p} - p_{0}}{\sqrt{p_{0} q_{0} / n}}$ $Test for p : z = \frac{\hat{p} - p_{0}}{\sqrt{p_{0} q_{0} / n}}$

$Test for σ^{2} : x^{2} = {(n - 1) s^{2} / (σ_{0})}^{2}$ $Test for σ^{2} : x^{2} = {(n - 1) s^{2} / (σ_{0})}^{2}$

Chapter 7

$CI for μ_{1} - μ_{2} :$ $CI for μ_{1} - μ_{2} :$

$({\bar{x}}_{1} - {\bar{x}}_{2}) \pm z_{α / 2} \sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}} (large n_{1} and n_{2})$ $({\bar{x}}_{1} - {\bar{x}}_{2}) \pm z_{α / 2} \sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}} (large n_{1} and n_{2})$

$Test for μ_{1} - μ_{2} :$ $Test for μ_{1} - μ_{2} :$

$z = \frac{({\bar{x}}_{1} - {\bar{x}}_{2}) - (μ_{1} - μ_{2})}{\sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}}} (large n_{1} and n_{2})$ $z = \frac{({\bar{x}}_{1} - {\bar{x}}_{2}) - (μ_{1} - μ_{2})}{\sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}}} (large n_{1} and n_{2})$

$s_{p}^{2} = \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2}$ $s_{p}^{2} = \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2}$

$CI for μ_{1} - μ_{2} :$ $CI for μ_{1} - μ_{2} :$

$({\bar{x}}_{1} - {\bar{x}}_{2}) \pm t_{α / 2} \sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}} (small n_{1} and/or n_{2})$ $({\bar{x}}_{1} - {\bar{x}}_{2}) \pm t_{α / 2} \sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}} (small n_{1} and/or n_{2})$

$Test for μ_{1} - μ_{2} :$ $Test for μ_{1} - μ_{2} :$

$t = \frac{({\bar{x}}_{1} - {\bar{x}}_{2}) - (μ_{1} - μ_{2})}{\sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}} (small n_{1} and/or n_{2})$ $t = \frac{({\bar{x}}_{1} - {\bar{x}}_{2}) - (μ_{1} - μ_{2})}{\sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}} (small n_{1} and/or n_{2})$

$CI for μ_{d} : {\bar{x}}_{d} \pm t_{α / 2} \frac{s_{d}}{\sqrt{n}}$ $CI for μ_{d} : {\bar{x}}_{d} \pm t_{α / 2} \frac{s_{d}}{\sqrt{n}}$

$Test for μ_{d} : t = \frac{{\bar{x}}_{d} - μ_{d}}{s_{d} / \sqrt{n}}$ $Test for μ_{d} : t = \frac{{\bar{x}}_{d} - μ_{d}}{s_{d} / \sqrt{n}}$

$Estimating μ_{1} - μ_{2} : n_{1} = n_{2} = {(z_{α / 2})}^{2} (σ_{1}^{2} + σ_{2}^{2}) / {(ME)}^{2}$ $Estimating μ_{1} - μ_{2} : n_{1} = n_{2} = {(z_{α / 2})}^{2} (σ_{1}^{2} + σ_{2}^{2}) / {(ME)}^{2}$

ANOVA Test:

$F = MST/MSE$ $F = MST/MSE$

Chapter 8

$CI for p_{1} - p_{2} : ({\hat{p}}_{1} - {\hat{p}}_{2}) \pm z_{α / 2} \sqrt{\frac{{\hat{p}}_{1} {\hat{q}}_{1}}{n_{1}} + \frac{{\hat{p}}_{2} {\hat{q}}_{2}}{n_{2}}}$ $CI for p_{1} - p_{2} : ({\hat{p}}_{1} - {\hat{p}}_{2}) \pm z_{α / 2} \sqrt{\frac{{\hat{p}}_{1} {\hat{q}}_{1}}{n_{1}} + \frac{{\hat{p}}_{2} {\hat{q}}_{2}}{n_{2}}}$

$Test for p_{1} - p_{2} : z = \frac{({\hat{p}}_{1} - {\hat{p}}_{2}) - (p_{1} - p_{2})}{\sqrt{\hat{p} \hat{q} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}$ $Test for p_{1} - p_{2} : z = \frac{({\hat{p}}_{1} - {\hat{p}}_{2}) - (p_{1} - p_{2})}{\sqrt{\hat{p} \hat{q} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}$

$\hat{p} = \frac{x_{1} + x_{2}}{n_{1} + n_{2}}$ $\hat{p} = \frac{x_{1} + x_{2}}{n_{1} + n_{2}}$

$Estimating p_{1} - p_{2} : n_{1} = n_{2} = {(z_{α / 2})}^{2} (p_{1} q_{1} + p_{2} q_{2}) / {(ME)}^{2}$ $Estimating p_{1} - p_{2} : n_{1} = n_{2} = {(z_{α / 2})}^{2} (p_{1} q_{1} + p_{2} q_{2}) / {(ME)}^{2}$

$Multinomial test: χ^{2} = \sum \frac{{(n_{i} - E_{i})}^{2}}{E_{i}}$ $Multinomial test: χ^{2} = \sum \frac{{(n_{i} - E_{i})}^{2}}{E_{i}}$

$E_{i} = n (p_{i 0})$ $E_{i} = n (p_{i 0})$

$Contingency table test: χ^{2} = \sum \frac{{(n_{i j} - E_{i j})}^{2}}{E_{i j}}$ $Contingency table test: χ^{2} = \sum \frac{{(n_{i j} - E_{i j})}^{2}}{E_{i j}}$

$E_{i j} = \frac{R_{i} C_{j}}{n}$ $E_{i j} = \frac{R_{i} C_{j}}{n}$

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for Selected Formulas

Create new playlist

Sign In

Sign Up

Table of Contents for
Selected Formulas