Which test to use for this scenario? A histogram of white blood cell (WBC) counts in 15 sick patients showed that the distribution was negatively skewed. If we wanted to test for differences between the published WBC count for a healthy population compared to the WBC values in these patients which type of test should be used?
Answer is saying Wilcoxon signed rank test rather than Mann-Whitney and i'm not sure why?
 A: Just realised the answer. It’s because the second group isn’t actually a group it’s a published average for the population. So it’s the non parametric version of the one sample t test rather than independent t test.
A: I have no idea what values you may have for WBC, but here is a left-skewed sample of size $n = 15$ with median around $H = 17.$ If the sample in your publication has population median around $\eta = 14,$ then your subjects are from a different population.
set.seed(2020)
x = 20*rbeta(15, 10, 2)
boxplot(x, horizontal=T)


summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  8.236  14.891  16.981  16.193  18.584  19.929 

wilcox.test(x, mu=14)

        Wilcoxon signed rank test

data:  x
V = 100, p-value = 0.02155
alternative hypothesis: true location is not equal to 14

The difference between 17 and 14 is relatively large. With only
$n= 15$ observations you may not have very good power (ability to
detect a real difference). For example:
wilcox.test(x, mu=15)$p.val
[1] 0.1069946

