{"id":539,"date":"2022-05-18T16:40:40","date_gmt":"2022-05-18T16:40:40","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/accintrostats\/back-matter\/mathematical-phrases-symbols-and-formulas\/"},"modified":"2022-05-18T16:40:40","modified_gmt":"2022-05-18T16:40:40","slug":"mathematical-phrases-symbols-and-formulas","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.ccconline.org\/accintrostats\/back-matter\/mathematical-phrases-symbols-and-formulas\/","title":{"raw":"Mathematical Phrases, Symbols, and Formulas","rendered":"Mathematical Phrases, Symbols, and Formulas"},"content":{"raw":" \n
\n

English Phrases Written Mathematically<\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
When the English says:<\/th>\nInterpret this as:<\/th>\n<\/tr>\n<\/thead>\n
X<\/em> is at least 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
The minimum of X<\/em> is 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is no less than 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is greater than or equal to 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is at most 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
The maximum of X<\/em> is 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is no more than 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is less than or equal to 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> does not exceed 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is greater than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is more than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> exceeds 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is less than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
There are fewer X<\/em> than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
X<\/em> is 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is equal to 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is the same as 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is not 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not equal to 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not the same as 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is different than 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

Formulas<\/h3>\n
\n

Formula 1: Factorial<\/h4>\n

\\(n!=n\\left(n-1\\right)\\left(n-2\\right)...\\left(1\\right)\\text{}\\)<\/p>\n

\\(0!=1\\text{}\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 2: Combinations<\/h4>\n

\\(\\left(\\begin{array}{l}n\\\\ r\\end{array}\\right)=\\frac{n!}{\\left(n-r\\right)!r!}\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 3: Binomial Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}B\\left(n,p\\right)\\)<\/p>\n

\\(P\\left(X=x\\right)=\\left(\\begin{array}{c}n\\\\ x\\end{array}\\right){p}^{x}{q}^{n-x}\\), for \\(x=0,1,2,...,n\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 4: Geometric Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}G\\left(p\\right)\\)<\/p>\n

\\(P\\left(X=x\\right)={q}^{x-1}p\\), for \\(x=1,2,3,...\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 5: Hypergeometric Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}H\\left(r,b,n\\right)\\)<\/p>\n

\\(P\\text{(}X=x\\text{)}=\\left(\\frac{\\left(\\genfrac{}{}{0}{}{r}{x}\\right)\\left(\\genfrac{}{}{0}{}{b}{n-x}\\right)}{\\left(\\genfrac{}{}{0}{}{r+b}{n}\\right)}\\right)\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 6: Poisson Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}P\\left(\\mu \\right)\\)<\/p>\n

\\(P\\text{(}X=x\\text{)}=\\frac{{\\mu }^{x}{e}^{-\\mu }}{x!}\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 7: Uniform Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}U\\left(a,b\\right)\\)<\/p>\n

\\(f\\left(X\\right)=\\frac{1}{b-a}\\), \\(a<x<b\\)\n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 8: Exponential Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}Exp\\left(m\\right)\\)<\/p>\n

\\(f\\left(x\\right)=m{e}^{-mx}m>0,x\\ge 0\\)\n\n<\/span><\/p>\n

Formula 9: Normal Distribution<\/span>\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}N\\left(\\mu ,{\\sigma }^{2}\\right)\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{1}{\\sigma \\sqrt{2\\pi }}{e}^{\\frac{{-\\left(x-\\mu \\right)}^{2}}{{2\\sigma }^{2}}}\\) , \\(\\phantom{\\rule{12pt}{0ex}}\u2013\\infty <x<\\infty \\) \n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 10: Gamma Function<\/h4>\n

\\(\\Gamma \\left(z\\right)=\\underset{\\infty }{\\overset{0}{{\\int }^{\\text{\u200b}}}}{x}^{z-1}{e}^{-x}dx\\)\\(z>0\\)<\/p>\n

\\(\\Gamma \\left(\\frac{1}{2}\\right)=\\sqrt{\\pi }\\)<\/p>\n

\\(\\Gamma \\left(m+1\\right)=m!\\) for \\(m\\), a nonnegative integer<\/p>\n

otherwise: \\(\\Gamma \\left(a+1\\right)=a\\Gamma \\left(a\\right)\\) \n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 11: Student's t<\/em>-distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{t}_{df}\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{{\\left(1+\\frac{{x}^{2}}{n}\\right)}^{\\frac{-\\left(n+1\\right)}{2}}\\Gamma \\left(\\frac{n+1}{2}\\right)}{\\sqrt{\\mathrm{n\\pi }}\\Gamma \\left(\\frac{n}{2}\\right)}\\)<\/p>\n

\\(X=\\frac{Z}{\\sqrt{\\frac{Y}{n}}}\\)<\/p>\n

\\(Z\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}N\\left(0,1\\right),\\phantom{\\rule{2px}{0ex}}Y\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{\u03a7}_{df}^{2}\\), \\(n\\) = degrees of freedom \n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 12: Chi-Square Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{\u03a7}_{df}^{2}\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{{x}^{\\frac{n-2}{2}}{e}^{\\frac{-x}{2}}}{{2}^{\\frac{n}{2}}\\Gamma \\left(\\frac{n}{2}\\right)}\\), \\(x>0\\) , \\(n\\) = positive integer and degrees of freedom \n\n<\/span><\/p>\n\n<\/div>\n

\n

Formula 13: F Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{F}_{df\\left(n\\right),df\\left(d\\right)}\\)<\/p>\n

\\(df\\left(n\\right)\\phantom{\\rule{2px}{0ex}}=\\phantom{\\rule{2px}{0ex}}\\)degrees of freedom for the numerator<\/p>\n

\\(df\\left(d\\right)\\phantom{\\rule{2px}{0ex}}=\\phantom{\\rule{2px}{0ex}}\\)degrees of freedom for the denominator<\/p>\n

\\(f\\left(x\\right)=\\frac{\\Gamma \\left(\\frac{u+v}{2}\\right)}{\\Gamma \\left(\\frac{u}{2}\\right)\\Gamma \\left(\\frac{v}{2}\\right)}{\\left(\\frac{u}{v}\\right)}^{\\frac{u}{2}}{x}^{\\left(\\frac{u}{2}-1\\right)}\\left[1+\\left(\\frac{u}{v}\\right){x}^{-0.5\\left(u+v\\right)}\\right]\\)<\/p>\n

\\(X=\\frac{{Y}_{u}}{{W}_{v}}\\), \\(Y\\), \\(W\\) are chi-square<\/p>\n\n<\/div>\n<\/div>\n

\n

Symbols and Their Meanings<\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Symbols and their Meanings<\/span><\/caption>\n
Chapter (1st used)<\/th>\nSymbol<\/th>\nSpoken<\/th>\nMeaning<\/th>\n<\/tr>\n<\/thead>\n
Sampling and Data<\/td>\n\\(\\sqrt{\\begin{array}{c}\\text{\u00a0\u00a0}\\\\ \\text{\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}\\end{array}}\\)<\/td>\nThe square root of<\/td>\nsame<\/td>\n<\/tr>\n
Sampling and Data<\/td>\n\\(\\pi \\)<\/td>\nPi<\/td>\n3.14159\u2026 (a specific number)<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>1<\/sub><\/td>\nQuartile one<\/td>\nthe first quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>2<\/sub><\/td>\nQuartile two<\/td>\nthe second quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>3<\/sub><\/td>\nQuartile three<\/td>\nthe third quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nIQR<\/em><\/td>\ninterquartile range<\/td>\nQ<\/em>3<\/sub> \u2013 Q<\/em>1<\/sub> = IQR<\/em><\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\overline{x}\\)<\/td>\nx-bar<\/td>\nsample mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\mu \\)<\/td>\nmu<\/td>\npopulation mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\ns<\/strong>sx<\/sub><\/em>sx<\/em><\/td>\ns<\/td>\nsample standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\({s}^{2}\\)\\({s}_{x}^{2}\\)<\/td>\ns squared<\/td>\nsample variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\sigma \\)\\({\\sigma }_{x}\\)\u03c3x<\/em><\/td>\nsigma<\/td>\npopulation standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\({\\sigma }^{2}\\)\\({\\sigma }_{x}^{2}\\)<\/td>\nsigma squared<\/td>\npopulation variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\Sigma \\)<\/td>\ncapital sigma<\/td>\nsum<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(\\left\\{\\right\\}\\)<\/td>\nbrackets<\/td>\nset notation<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(S\\)<\/td>\nS<\/td>\nsample space<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(A\\)<\/td>\nEvent A<\/td>\nevent A<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\right)\\)<\/td>\nprobability of A<\/td>\nprobability of A occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(\\mathit{\\text{A}}\\text{|}\\mathit{\\text{B}}\\right)\\)<\/td>\nprobability of A given B<\/td>\nprob. of A occurring given B has occurred<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\text{\u00a0OR\u00a0}B\\right)\\)<\/td>\nprob. of A or B<\/td>\nprob. of A or B or both occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\text{\u00a0AND\u00a0}B\\right)\\)<\/td>\nprob. of A and B<\/td>\nprob. of both A and B occurring (same time)<\/td>\n<\/tr>\n
Probability Topics<\/td>\nA<\/em>\u2032<\/td>\nA-prime, complement of A<\/td>\ncomplement of A, not A<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(A<\/em>')<\/td>\nprob. of complement of A<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nG<\/em>1<\/sub><\/td>\ngreen on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(G<\/em>1<\/sub>)<\/td>\nprob. of green on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nPDF<\/em><\/td>\nprob. distribution function<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em><\/td>\nX<\/td>\nthe random variable X<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em> ~<\/td>\nthe distribution of X<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nB<\/em><\/td>\nbinomial distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nG<\/em><\/td>\ngeometric distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nH<\/em><\/td>\nhypergeometric dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nP<\/em><\/td>\nPoisson dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\lambda \\)<\/td>\nLambda<\/td>\naverage of Poisson distribution<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\ge \\)<\/td>\ngreater than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\le \\)<\/td>\nless than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n=<\/td>\nequal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\u2260<\/td>\nnot equal to<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>)<\/td>\nf<\/em> of x<\/em><\/td>\nfunction of x<\/em><\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\npdf<\/em><\/td>\nprob. density function<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nU<\/em><\/td>\nuniform distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nExp<\/em><\/td>\nexponential distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nk<\/em><\/td>\nk<\/em><\/td>\ncritical value<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>) =<\/td>\nf<\/em> of x<\/em> equals<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nm<\/em><\/td>\nm<\/em><\/td>\ndecay rate (for exp. dist.)<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nN<\/em><\/td>\nnormal distribution<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nz<\/em><\/td>\nz<\/em>-score<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nZ<\/em><\/td>\nstandard normal dist.<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\nCLT<\/em><\/td>\nCentral Limit Theorem<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\overline{X}\\)<\/td>\nX<\/em>-bar<\/td>\nthe random variable X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\mu }_{x}\\)<\/td>\nmean of X<\/em><\/td>\nthe average of X<\/em><\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\mu }_{\\overline{x}}\\)<\/td>\nmean of X<\/em>-bar<\/td>\nthe average of X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\sigma }_{x}\\)<\/td>\nstandard deviation of X<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\sigma }_{\\overline{x}}\\)<\/td>\nstandard deviation of X<\/em>-bar<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\Sigma X\\)<\/td>\nsum of X<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\Sigma x\\)<\/td>\nsum of x<\/em><\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCL<\/em><\/td>\nconfidence level<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCI<\/em><\/td>\nconfidence interval<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBM<\/em><\/td>\nerror bound for a mean<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBP<\/em><\/td>\nerror bound for a proportion<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nt<\/em><\/td>\nStudent's t<\/em>-distribution<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\ndf<\/em><\/td>\ndegrees of freedom<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\({t}_{\\frac{\\alpha }{2}}\\)<\/td>\nstudent t with a<\/em>\/2 area in right tail<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\(p\\prime \\); \\(\\stackrel{^}{p}\\)<\/td>\np<\/em>-prime; p<\/em>-hat<\/td>\nsample proportion of success<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\(q\\prime \\); \\(\\stackrel{^}{q}\\)<\/td>\nq<\/em>-prime; q<\/em>-hat<\/td>\nsample proportion of failure<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{0}\\)<\/td>\nH<\/em>-naught, H<\/em>-sub 0<\/td>\nnull hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{a}\\)<\/td>\nH-a<\/em>, H<\/em>-sub a<\/em><\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{1}\\)<\/td>\nH<\/em>-1, H<\/em>-sub 1<\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\alpha \\)<\/td>\nalpha<\/td>\nprobability of Type I error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\beta \\)<\/td>\nbeta<\/td>\nprobability of Type II error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\overline{X1}-\\overline{X2}\\)<\/td>\nX<\/em>1-bar minus X<\/em>2-bar<\/td>\ndifference in sample means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({\\mu }_{1}-{\\mu }_{2}\\)<\/td>\nmu<\/em>-1 minus mu<\/em>-2<\/td>\ndifference in population means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({{P}^{\\prime }}_{1}-{{P}^{\\prime }}_{2}\\)<\/td>\nP<\/em>1-prime minus P<\/em>2-prime<\/td>\ndifference in sample proportions<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({p}_{1}-{p}_{2}\\)<\/td>\np<\/em>1 minus p<\/em>2<\/td>\ndifference in population proportions<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\({\u03a7}^{2}\\)<\/td>\nKy<\/em>-square<\/td>\nChi-square<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\(O\\)<\/td>\nObserved<\/td>\nObserved frequency<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\(E\\)<\/td>\nExpected<\/td>\nExpected frequency<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\ny<\/em> = a<\/em> + bx<\/em><\/td>\ny<\/em> equals a plus b-x<\/em><\/td>\nequation of a line<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(\\stackrel{^}{y}\\)<\/td>\ny<\/em>-hat<\/td>\nestimated value of y<\/em><\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(r\\)<\/td>\ncorrelation coefficient<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(\\epsilon \\)<\/td>\nerror<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\nSSE<\/em><\/td>\nSum of Squared Errors<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n1.9s<\/em><\/td>\n1.9 times s<\/em><\/td>\ncut-off value for outliers<\/td>\n<\/tr>\n
F<\/em>-Distribution and ANOVA<\/td>\nF<\/em><\/td>\nF<\/em>-ratio<\/td>\nF<\/em>-ratio<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>","rendered":"

 <\/p>\n

\n

English Phrases Written Mathematically<\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
When the English says:<\/th>\nInterpret this as:<\/th>\n<\/tr>\n<\/thead>\n
X<\/em> is at least 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
The minimum of X<\/em> is 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is no less than 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is greater than or equal to 4.<\/td>\nX<\/em> \u2265 4<\/td>\n<\/tr>\n
X<\/em> is at most 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
The maximum of X<\/em> is 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is no more than 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is less than or equal to 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> does not exceed 4.<\/td>\nX<\/em> \u2264 4<\/td>\n<\/tr>\n
X<\/em> is greater than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is more than 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> exceeds 4.<\/td>\nX<\/em> > 4<\/td>\n<\/tr>\n
X<\/em> is less than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
There are fewer X<\/em> than 4.<\/td>\nX<\/em> < 4<\/td>\n<\/tr>\n
X<\/em> is 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is equal to 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is the same as 4.<\/td>\nX<\/em> = 4<\/td>\n<\/tr>\n
X<\/em> is not 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not equal to 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is not the same as 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n
X<\/em> is different than 4.<\/td>\nX<\/em> \u2260 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

Formulas<\/h3>\n
\n

Formula 1: Factorial<\/h4>\n

\\(n!=n\\left(n-1\\right)\\left(n-2\\right)…\\left(1\\right)\\text{}\\)<\/p>\n

\\(0!=1\\text{}\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 2: Combinations<\/h4>\n

\\(\\left(\\begin{array}{l}n\\\\ r\\end{array}\\right)=\\frac{n!}{\\left(n-r\\right)!r!}\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 3: Binomial Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}B\\left(n,p\\right)\\)<\/p>\n

\\(P\\left(X=x\\right)=\\left(\\begin{array}{c}n\\\\ x\\end{array}\\right){p}^{x}{q}^{n-x}\\), for \\(x=0,1,2,…,n\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 4: Geometric Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}G\\left(p\\right)\\)<\/p>\n

\\(P\\left(X=x\\right)={q}^{x-1}p\\), for \\(x=1,2,3,…\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 5: Hypergeometric Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}H\\left(r,b,n\\right)\\)<\/p>\n

\\(P\\text{(}X=x\\text{)}=\\left(\\frac{\\left(\\genfrac{}{}{0}{}{r}{x}\\right)\\left(\\genfrac{}{}{0}{}{b}{n-x}\\right)}{\\left(\\genfrac{}{}{0}{}{r+b}{n}\\right)}\\right)\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 6: Poisson Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}P\\left(\\mu \\right)\\)<\/p>\n

\\(P\\text{(}X=x\\text{)}=\\frac{{\\mu }^{x}{e}^{-\\mu }}{x!}\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 7: Uniform Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}U\\left(a,b\\right)\\)<\/p>\n

\\(f\\left(X\\right)=\\frac{1}{b-a}\\), \\(a<x<b\\)<\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 8: Exponential Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}Exp\\left(m\\right)\\)<\/p>\n

\\(f\\left(x\\right)=m{e}^{-mx}m>0,x\\ge 0\\)<\/p>\n

<\/span><\/p>\n

Formula 9: Normal Distribution<\/span>\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}N\\left(\\mu ,{\\sigma }^{2}\\right)\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{1}{\\sigma \\sqrt{2\\pi }}{e}^{\\frac{{-\\left(x-\\mu \\right)}^{2}}{{2\\sigma }^{2}}}\\) , \\(\\phantom{\\rule{12pt}{0ex}}\u2013\\infty <x<\\infty \\) <\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 10: Gamma Function<\/h4>\n

\\(\\Gamma \\left(z\\right)=\\underset{\\infty }{\\overset{0}{{\\int }^{\\text{\u200b}}}}{x}^{z-1}{e}^{-x}dx\\)\\(z>0\\)<\/p>\n

\\(\\Gamma \\left(\\frac{1}{2}\\right)=\\sqrt{\\pi }\\)<\/p>\n

\\(\\Gamma \\left(m+1\\right)=m!\\) for \\(m\\), a nonnegative integer<\/p>\n

otherwise: \\(\\Gamma \\left(a+1\\right)=a\\Gamma \\left(a\\right)\\) <\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 11: Student’s t<\/em>-distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{t}_{df}\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{{\\left(1+\\frac{{x}^{2}}{n}\\right)}^{\\frac{-\\left(n+1\\right)}{2}}\\Gamma \\left(\\frac{n+1}{2}\\right)}{\\sqrt{\\mathrm{n\\pi }}\\Gamma \\left(\\frac{n}{2}\\right)}\\)<\/p>\n

\\(X=\\frac{Z}{\\sqrt{\\frac{Y}{n}}}\\)<\/p>\n

\\(Z\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}N\\left(0,1\\right),\\phantom{\\rule{2px}{0ex}}Y\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{\u03a7}_{df}^{2}\\), \\(n\\) = degrees of freedom <\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 12: Chi-Square Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{\u03a7}_{df}^{2}\\)<\/p>\n

\\(f\\text{(}x\\text{)}=\\frac{{x}^{\\frac{n-2}{2}}{e}^{\\frac{-x}{2}}}{{2}^{\\frac{n}{2}}\\Gamma \\left(\\frac{n}{2}\\right)}\\), \\(x>0\\) , \\(n\\) = positive integer and degrees of freedom <\/p>\n

<\/span><\/p>\n<\/div>\n

\n

Formula 13: F Distribution<\/h4>\n

\\(X\\phantom{\\rule{2px}{0ex}}~\\phantom{\\rule{2px}{0ex}}{F}_{df\\left(n\\right),df\\left(d\\right)}\\)<\/p>\n

\\(df\\left(n\\right)\\phantom{\\rule{2px}{0ex}}=\\phantom{\\rule{2px}{0ex}}\\)degrees of freedom for the numerator<\/p>\n

\\(df\\left(d\\right)\\phantom{\\rule{2px}{0ex}}=\\phantom{\\rule{2px}{0ex}}\\)degrees of freedom for the denominator<\/p>\n

\\(f\\left(x\\right)=\\frac{\\Gamma \\left(\\frac{u+v}{2}\\right)}{\\Gamma \\left(\\frac{u}{2}\\right)\\Gamma \\left(\\frac{v}{2}\\right)}{\\left(\\frac{u}{v}\\right)}^{\\frac{u}{2}}{x}^{\\left(\\frac{u}{2}-1\\right)}\\left[1+\\left(\\frac{u}{v}\\right){x}^{-0.5\\left(u+v\\right)}\\right]\\)<\/p>\n

\\(X=\\frac{{Y}_{u}}{{W}_{v}}\\), \\(Y\\), \\(W\\) are chi-square<\/p>\n<\/div>\n<\/div>\n

\n

Symbols and Their Meanings<\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Symbols and their Meanings<\/span><\/caption>\n
Chapter (1st used)<\/th>\nSymbol<\/th>\nSpoken<\/th>\nMeaning<\/th>\n<\/tr>\n<\/thead>\n
Sampling and Data<\/td>\n\\(\\sqrt{\\begin{array}{c}\\text{\u00a0\u00a0}\\\\ \\text{\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}\\end{array}}\\)<\/td>\nThe square root of<\/td>\nsame<\/td>\n<\/tr>\n
Sampling and Data<\/td>\n\\(\\pi \\)<\/td>\nPi<\/td>\n3.14159\u2026 (a specific number)<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>1<\/sub><\/td>\nQuartile one<\/td>\nthe first quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>2<\/sub><\/td>\nQuartile two<\/td>\nthe second quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nQ<\/em>3<\/sub><\/td>\nQuartile three<\/td>\nthe third quartile<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\nIQR<\/em><\/td>\ninterquartile range<\/td>\nQ<\/em>3<\/sub> \u2013 Q<\/em>1<\/sub> = IQR<\/em><\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\overline{x}\\)<\/td>\nx-bar<\/td>\nsample mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\mu \\)<\/td>\nmu<\/td>\npopulation mean<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\ns<\/strong>sx<\/sub><\/em>sx<\/em><\/td>\ns<\/td>\nsample standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\({s}^{2}\\)\\({s}_{x}^{2}\\)<\/td>\ns squared<\/td>\nsample variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\sigma \\)\\({\\sigma }_{x}\\)\u03c3x<\/em><\/td>\nsigma<\/td>\npopulation standard deviation<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\({\\sigma }^{2}\\)\\({\\sigma }_{x}^{2}\\)<\/td>\nsigma squared<\/td>\npopulation variance<\/td>\n<\/tr>\n
Descriptive Statistics<\/td>\n\\(\\Sigma \\)<\/td>\ncapital sigma<\/td>\nsum<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(\\left\\{\\right\\}\\)<\/td>\nbrackets<\/td>\nset notation<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(S\\)<\/td>\nS<\/td>\nsample space<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(A\\)<\/td>\nEvent A<\/td>\nevent A<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\right)\\)<\/td>\nprobability of A<\/td>\nprobability of A occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(\\mathit{\\text{A}}\\text{|}\\mathit{\\text{B}}\\right)\\)<\/td>\nprobability of A given B<\/td>\nprob. of A occurring given B has occurred<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\text{\u00a0OR\u00a0}B\\right)\\)<\/td>\nprob. of A or B<\/td>\nprob. of A or B or both occurring<\/td>\n<\/tr>\n
Probability Topics<\/td>\n\\(P\\left(A\\text{\u00a0AND\u00a0}B\\right)\\)<\/td>\nprob. of A and B<\/td>\nprob. of both A and B occurring (same time)<\/td>\n<\/tr>\n
Probability Topics<\/td>\nA<\/em>\u2032<\/td>\nA-prime, complement of A<\/td>\ncomplement of A, not A<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(A<\/em>‘)<\/td>\nprob. of complement of A<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nG<\/em>1<\/sub><\/td>\ngreen on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Probability Topics<\/td>\nP<\/em>(G<\/em>1<\/sub>)<\/td>\nprob. of green on first pick<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nPDF<\/em><\/td>\nprob. distribution function<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em><\/td>\nX<\/td>\nthe random variable X<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nX<\/em> ~<\/td>\nthe distribution of X<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nB<\/em><\/td>\nbinomial distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nG<\/em><\/td>\ngeometric distribution<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nH<\/em><\/td>\nhypergeometric dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\nP<\/em><\/td>\nPoisson dist.<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\lambda \\)<\/td>\nLambda<\/td>\naverage of Poisson distribution<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\ge \\)<\/td>\ngreater than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\\(\\le \\)<\/td>\nless than or equal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n=<\/td>\nequal to<\/td>\nsame<\/td>\n<\/tr>\n
Discrete Random Variables<\/td>\n\u2260<\/td>\nnot equal to<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>)<\/td>\nf<\/em> of x<\/em><\/td>\nfunction of x<\/em><\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\npdf<\/em><\/td>\nprob. density function<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nU<\/em><\/td>\nuniform distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nExp<\/em><\/td>\nexponential distribution<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nk<\/em><\/td>\nk<\/em><\/td>\ncritical value<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nf<\/em>(x<\/em>) =<\/td>\nf<\/em> of x<\/em> equals<\/td>\nsame<\/td>\n<\/tr>\n
Continuous Random Variables<\/td>\nm<\/em><\/td>\nm<\/em><\/td>\ndecay rate (for exp. dist.)<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nN<\/em><\/td>\nnormal distribution<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nz<\/em><\/td>\nz<\/em>-score<\/td>\nsame<\/td>\n<\/tr>\n
The Normal Distribution<\/td>\nZ<\/em><\/td>\nstandard normal dist.<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\nCLT<\/em><\/td>\nCentral Limit Theorem<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\overline{X}\\)<\/td>\nX<\/em>-bar<\/td>\nthe random variable X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\mu }_{x}\\)<\/td>\nmean of X<\/em><\/td>\nthe average of X<\/em><\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\mu }_{\\overline{x}}\\)<\/td>\nmean of X<\/em>-bar<\/td>\nthe average of X<\/em>-bar<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\sigma }_{x}\\)<\/td>\nstandard deviation of X<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\({\\sigma }_{\\overline{x}}\\)<\/td>\nstandard deviation of X<\/em>-bar<\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\Sigma X\\)<\/td>\nsum of X<\/em><\/td>\nsame<\/td>\n<\/tr>\n
The Central Limit Theorem<\/td>\n\\(\\Sigma x\\)<\/td>\nsum of x<\/em><\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCL<\/em><\/td>\nconfidence level<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nCI<\/em><\/td>\nconfidence interval<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBM<\/em><\/td>\nerror bound for a mean<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nEBP<\/em><\/td>\nerror bound for a proportion<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\nt<\/em><\/td>\nStudent’s t<\/em>-distribution<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\ndf<\/em><\/td>\ndegrees of freedom<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\({t}_{\\frac{\\alpha }{2}}\\)<\/td>\nstudent t with a<\/em>\/2 area in right tail<\/td>\nsame<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\(p\\prime \\); \\(\\stackrel{^}{p}\\)<\/td>\np<\/em>-prime; p<\/em>-hat<\/td>\nsample proportion of success<\/td>\n<\/tr>\n
Confidence Intervals<\/td>\n\\(q\\prime \\); \\(\\stackrel{^}{q}\\)<\/td>\nq<\/em>-prime; q<\/em>-hat<\/td>\nsample proportion of failure<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{0}\\)<\/td>\nH<\/em>-naught, H<\/em>-sub 0<\/td>\nnull hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{a}\\)<\/td>\nH-a<\/em>, H<\/em>-sub a<\/em><\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({H}_{1}\\)<\/td>\nH<\/em>-1, H<\/em>-sub 1<\/td>\nalternate hypothesis<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\alpha \\)<\/td>\nalpha<\/td>\nprobability of Type I error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\beta \\)<\/td>\nbeta<\/td>\nprobability of Type II error<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\(\\overline{X1}-\\overline{X2}\\)<\/td>\nX<\/em>1-bar minus X<\/em>2-bar<\/td>\ndifference in sample means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({\\mu }_{1}-{\\mu }_{2}\\)<\/td>\nmu<\/em>-1 minus mu<\/em>-2<\/td>\ndifference in population means<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({{P}^{\\prime }}_{1}-{{P}^{\\prime }}_{2}\\)<\/td>\nP<\/em>1-prime minus P<\/em>2-prime<\/td>\ndifference in sample proportions<\/td>\n<\/tr>\n
Hypothesis Testing<\/td>\n\\({p}_{1}-{p}_{2}\\)<\/td>\np<\/em>1 minus p<\/em>2<\/td>\ndifference in population proportions<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\({\u03a7}^{2}\\)<\/td>\nKy<\/em>-square<\/td>\nChi-square<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\(O\\)<\/td>\nObserved<\/td>\nObserved frequency<\/td>\n<\/tr>\n
Chi-Square Distribution<\/td>\n\\(E\\)<\/td>\nExpected<\/td>\nExpected frequency<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\ny<\/em> = a<\/em> + bx<\/em><\/td>\ny<\/em> equals a plus b-x<\/em><\/td>\nequation of a line<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(\\stackrel{^}{y}\\)<\/td>\ny<\/em>-hat<\/td>\nestimated value of y<\/em><\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(r\\)<\/td>\ncorrelation coefficient<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n\\(\\epsilon \\)<\/td>\nerror<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\nSSE<\/em><\/td>\nSum of Squared Errors<\/td>\nsame<\/td>\n<\/tr>\n
Linear Regression and Correlation<\/td>\n1.9s<\/em><\/td>\n1.9 times s<\/em><\/td>\ncut-off value for outliers<\/td>\n<\/tr>\n
F<\/em>-Distribution and ANOVA<\/td>\nF<\/em><\/td>\nF<\/em>-ratio<\/td>\nF<\/em>-ratio<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"author":32,"menu_order":100,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-539","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/back-matter\/539","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/users\/32"}],"version-history":[{"count":0,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/back-matter\/539\/revisions"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/back-matter\/539\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/media?parent=539"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/pressbooks\/v2\/back-matter-type?post=539"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/contributor?post=539"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/accintrostats\/wp-json\/wp\/v2\/license?post=539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}