Conducting hypothesis testing

Population Mean

$$\mu_x$$

Population Standard Deviation

$$\sigma_x$$

Sample Mean

$\bar x$ or $M_x$

RSD Of Means (Random Sampling Distribution)

$M_{\bar{x}}$ (Same as population mean)

Standard Error Formula

$$\sigma_{\bar{x}}=\frac{\sigma_{x}}{\sqrt{n}}$$

number to Z-stat

$$z=\frac{x-\mu}{\sigma}$$

Z-stat to number

$$x=z\sigma+\mu$$

Confidence intervals (z-stat to number)

$$\bar{x}_{upper or lower}=\pm{z}(\sigma_{\bar{x}})+\bar{x}$$

Cohen’s d

$$d=\frac{\bar{x}-\mu_{x}}{\sigma_{x}}$$

Mean Difference

$$\bar{x}_{D}=\frac{\sum{x_{D}}}{n}$$

Sample standard deviation

$$S_{D}=\frac{\sum{(x-\bar{x})^{2}}}{n-1}$$

RSD of Mean Differences (Random sampling distribution)

$M_{\bar{D}}$ (Same as population for null hypothesis or 0)

Degrees of freedom

$$df=N-1$$

Calculating T test statistic

$$t=\frac{\bar{x}_{D}-M_{\bar{D}}}{S_{\bar{D}}}$$