MATH 1530

Unit 4 Formula Sheet

Chapter 7

Test Statistics:

Mean: \(t=\frac{{\displaystyle\overset\_x}-\mu}{ \frac {s}{\sqrt n}}\)

Proportion: \(z=\frac{{\displaystyle\widehat p}-\mu_{\displaystyle\widehat p}}{\sigma_{\displaystyle\widehat p}}=\frac{\widehat p-p}{\sqrt{ \frac {pq}{n}}}\)

Chapter 9

Correlation Coefficient:

\(r=\frac{n\sum xy-\left(\sum x\right)\left(\sum y\right)}{\sqrt{n\sum x^2-\left(\sum x\right)^2}\sqrt{n\sum y^2-\left(\sum y\right)^2}}\)

t-Test for Linear Correlation:

\(t=\frac r{\sqrt{\displaystyle\frac{1-r^2}{n-2}}}\) (\(\text {degrees of freedom} = n-2\))

Equation of a Regression Line:

\(\widehat y=mx+b\)

Chapter 10:

Chi-Square

\(\chi^2={\textstyle\sum }\frac{\left(O-E\right)^2}E\)

Goodness of Fit Test:

degrees of freedom = \(k-1\)

Independence Test:

degrees of freedom = \((r-1)(c-1)\)

r=number of rows

c=number of columns

Table of Critical Values Pearson Correlation

2-tailed: Degrees of Freedom \(= n-2\)