The result is shown below. We can say the difference is significant.
However, now we need to re-think our H1 hypothesis 'younger people move longer distance', which is not true in terms of the average trip distance in our sample. On the contrary, Average Distance: Old = 0.01488, Young = 0.01439. Therefore, this result of t-test implies that older group has significantly longer average trip distance than that of the younger group. However, we should not change the hypotheses after starting analysis as we should be hypothesis-driven.
Conclusions -
We got the result above which is not intuitive. Therefore, we examined with different data set to check robustness. Using Citibike data of June 2015, we carried out the same experiment. Again, the average trip distance in the older group is longer than that of younger, and we got p-value of 0.59, which is not significant.
While we assumed that the younger ride longer distance, the result was opposite, which makes this research complicated.
Acknowledgments
My referee gave me several insightful advise and I am happy to follow his advises as I agree with his opinions. He recommended me to do t-test. I agree with that because we compare the means of two samples and can use a parametric test as the population is large enough. Also, he recommended me to add a figure which compares two means directly. As this may clarify the difference of two sample means, I added the figure 1. While he recommended me to slightly change the way to express H0 and H1 equations, I think either of my expression and his expression is fine.
GitHub link - Notebook