I have the following data on duration that different aged adults can remain standing.

$\begin{array}{|cccc|}\hline \text{Age}& \text{Sample Size}& \text{Sample Mean}& \text{Sample Std Dev}\\ \text{Old}& 28& 801& 117\\ \text{Young}& 16& 780& 72\\ \hline\end{array}$

The data I'm using has a normal distribution with the same variances. I want to do a test of hypotheses however at a significance level of 5% (a=0.05) to be able to confirm whether or not the average duration that older adults can remain standing is larger than among younger adults.

I'm not sure which of the different formulas I should use however to determine this due to my sample size being relatively small. Should I be using the following test.

to compute pooled standard deviation: ${s}^{2}=\frac{(1-1)s{1}^{2}+(n2-1)s{2}^{2}}{n1+n2-2}$

compute test statistics: $t=\frac{y1-y2-0}{s\sqrt{\frac{1}{n1}+\frac{1}{n2}}}$

$\begin{array}{|cccc|}\hline \text{Age}& \text{Sample Size}& \text{Sample Mean}& \text{Sample Std Dev}\\ \text{Old}& 28& 801& 117\\ \text{Young}& 16& 780& 72\\ \hline\end{array}$

The data I'm using has a normal distribution with the same variances. I want to do a test of hypotheses however at a significance level of 5% (a=0.05) to be able to confirm whether or not the average duration that older adults can remain standing is larger than among younger adults.

I'm not sure which of the different formulas I should use however to determine this due to my sample size being relatively small. Should I be using the following test.

to compute pooled standard deviation: ${s}^{2}=\frac{(1-1)s{1}^{2}+(n2-1)s{2}^{2}}{n1+n2-2}$

compute test statistics: $t=\frac{y1-y2-0}{s\sqrt{\frac{1}{n1}+\frac{1}{n2}}}$