Question

Assuming the population variances are unknown and equal, you wish to test whether the Group 1 population mean is equal to the Group 2 population mean. The resulting test statistic is a Student-t with how many degrees of freedom

Answer 1

Answer:

$n_1+n_2-2$

Step-by-step explanation:

If we had 2 independent samples with population variances unknown and equal and we want to compare the population mean between the both groups, the test statistic will be:

$t=\frac{x_1-x_2}{\sqrt{s_p^2(\frac{1}{n_1}+\frac{1}{n_2}) } }$

Where $s_p^2=\frac{(n_1-1)*s_1^2+(n_2-2)*s_2^2}{n_1+n_2-2}$

So, the t-student has $n_1+n_2-2$ degrees of freedom

Where $x_1$ and $x_2$ are the means of the groups, $n_1$ and $n_2$ are the size of the samples and $s_1^2$ and $s_2^2$ are the sample variances.