One Sample t-Test

Conceptual: Formulas

Which t-score formula is the correct one for a one-sample test?

A) $t = \frac{\bar{y}- m_0}{\hat{\sigma}/\sqrt{n}}$

Such that:

$\bar{y} =$ sample mean

$m_0 =$ population mean/hypothesized value

$\hat{\sigma} =$ sample standard deviation

$n =$ sample size

B) $t=\frac{\bar{Y_1}−\bar{Y_2}}{\sqrt{s_1^2/N_1+s_2^2/N_2}}$

Such that:

$N_1$ and $N_2$ are the sample sizes

$\bar{Y_1}$ and $\bar{Y_2}$ are the sample means

$\bar{s_1}^2$ and $\bar{s_2}^2$ are the sample variances.