Given a sample population of 54 men and 61 women, I want to figure out whether or not the average male spends less time during his daily shower than the average female spends during hers. The average male time is 2.9 minutes with a standard deviation of 0.65 minutes. The average female time is 3.31 minutes and the standard deviation is 0.71 minutes.
I am trying to figure out the test statistic and P-value for this test. I was under the impression that when comparing two populations, you should use the following formula to obtain a test statistic:
$$\frac{\hat{p}_x - \hat{p}_y}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_x} +\frac{1}{n_y})}}$$
But because $p$ deals with proportions I'm not sure how to implement it in this case. Any help would be appreciated.