Average trip duration in July 2017 is greater across both payment classes compared to average trip duration in January 2017. For January however, the difference in trip duration across the two payment classes is much smaller, which results in us not being able to reject our null hypothesis.
Methodology:
To test the null hypothesis given the type of data analyzed and the question asked, we prefer to utilize the t-test. We noted that the data has means for two groups for where both the t-test and z-test could be applied. The t-test was the better selection in our opinion as we had two groups with no standard deviation valuation of the population. The t-test has a better application than the z-test because the uncertainty in the sample variance is not accounted for as the z-test is incorporated.
Conclusions:
Based on the outcome of the t-test, we could not reject the null hypothesis for the month of January, but we could reject the null hypothesis for the month of July.
This conclusion was supported by the results of the t-test, which showed a significance level of 0.17 for the month of January, and a much lower 2.08 x 10^-244 for the month of July. In plain figures, we could see this illustrated by the difference in the means for the two months (see figures 3 and 4 below).