Your data are paired, so the Mann-Whitney U test (which isn't) is immediately out.
We can easily argue for normality (the counts are large, if "$k$" means thousands, so near-normality would be reasonable), but the actual problem is that since for count data we expect the variance to be related to the mean, unless we assume that the mean isn't varying across days, we don't have constant variance, which might suggest some caution with the t-test; it will still have decent power, but its type I error rate may be somewhat affected.
You can argue for the Wilcoxon signed rank test, but there are several issues there that need to be thought about.
Note that there's also the sign test.
One could easily argue for a test that's appropriate for count data. So, for example, you could do a form of proportion test that takes account of the apparent one-tailedness of the hypothesis. (If you do a two-tailed test, you could also do it as a chi-square.)
Finally, one could also fit a Poisson, quasi-Poisson or Negative Binomial GLM.
In scipy.stats, the Mann-Whitney U test compares two populations:
Computes the Mann-Whitney rank test on samples x and y.
but the Wilcoxon test compares two PAIRED populations:
The Wilcoxon signed-rank test tests the null hypothesis that two
related paired samples come from the same distribution. In particular,
it tests whether the distribution of the differences x - y is
symmetric about zero. It is a non-parametric version of the paired
T-test.
EDITED / CORRECTED in response to ttnphns' comments.
Note that the t does not test for whether the distribution of the differences is symmetric about zero, so the Wilcoxon signed rank test is not truly a non-parametric counterpart of the paired t test.
The Mann-Whitney test, on the other hand, assumes that all the observations are independent of each other (no basis for pairing here!). It also assumes that the two distributions are the same, and the alternative is that one is stochastically greater than the other. If we make the additional assumption that the only difference between the two distributions is their location, and the distributions are continuous, then "stochastically greater than" is equivalent to such statements as "the medians are different", so you can, with the extra assumption(s), interpret it that way.
The Mann-Whitney uses a continuity correction by default, but the Wilcoxon doesn't.
The Mann-Whitney handles ties using the midrank, but the Wilcoxon offers three options for handling ties in the paired values (i.e., zero difference between the two elements of the pair.)
It sounds like the Wilcoxon test is the more appropriate for your purposes, since you do have that lack of independence between all observations. However, one might imagine that requests with similar, but not equal, lengths might exhibit similar behavior, whereas the Wilcoxon would assume that if they aren't paired, they are independent. A logistic regression model might serve you better in this case.
Quotes are from the scipy.stats doc pages, which we aren't supposed to link to, apparently.
Best Answer
There are two Wilcoxon tests, which can lead to some confusion. However, both are non-parametric tests that are not median value tests but are difference of locations tests. The Wilcoxon rank-sum test is often called the Mann-Whitney U test and is used to compare independent random variables. Click on that link to find out more about what that test does. Briefly, this tests the whether two groups of subjects with unequal numbers of subjects in each group, have the same location. It is not sensitive to non-normal conditions, thus its popularity.
Interpretation: As a test of location, one tests whether the data location is the same for two independent populations. The null hypothesis implies that there is a significant difference in location of the populations, and the alternative hypothesis implies that a significant difference was not detected under the conditions of the test. When the probability of this test is low [most often $p<0.05$, with a Type I error (AKA alpha, false positive rate) set at 0.05] we would accept the null (H0) hypothesis as the likelihood of the alternative hypothesis (H1) is low.
The second test is for paired data, and it compares "before" and "after" effects on the same subjects. This is called the Wilcoxon signed-rank test, which is not a synonym for the other Wilcoxon test, the Wilcoxon rank-sum test. The interpretation of this test is similar that of the other test above with the exception that there is no independence, the test is more sensitive for detecting differences, and the data has the same number of "participants" in both groups.
The Mann-Whitney U test uses the U-statistic as a measure of location. "U" stands for Unbiased. Such statistics arise in the context of minimum variance unbiased estimators, or UVME for short. The U-statistic has the property that the average over sample values $ƒ_n(x\phi)$ is exactly equal to the population value $ƒ_N(x)$ for a simple random sample $\phi$ of size $n$ taken from a population of size $N$.
Keep in mind that the Mann-Whitney U test is non-parametric, that is, it uses yes/no comparisons between entries and not distances. The U statistic, for that test, corresponds to the number of wins (> versus <) out of all pairwise contests. For each observation in one set, count the number of times this first value wins over any observations in the other set (the other value loses if this first is larger). Count 0.5 for any ties. The sum of wins and ties is U for the first set. U for the other set is the converse. One then uses a lookup table to convert U into probabilities. For larger sample size, say >20, there is a normal approximation for p(U).
This test works because the group of binary comparisons used results in a symmetric distribution for which the probabilities of difference of locations are calculable, even though the original data may consist of two asymmetrically distributed populations for which probabilities of difference of location are not easily calculable. Since the entries must be amenable to comparison of the >, < or = type, at least ordinal data is required, where by ordinal we mean non-parametric data for which > and < is a property, e.g., "How do you like my answer?" 1) Very dissatisfied 2) Somewhat dissatisfied 3) So-so 4) Somewhat satisfied 5) Very satisfied.