2 Questions for you lot. One I don't really know and one that I'm struggling to unravel my thoughts with...

First one that I'm unsure of...

Let be a strictly increasing function of a real variable. Show that the result of applying the sign test to a sample with hypothetical median is identical to that of applying the test to the transformed sample with hypothetical median .

And the other one

Consider a random sample from an unknown distribution where is unknown and , i.e. is the population median. Show that the Hodges-Lehmann point estimate of arising from the Sign Test is the sample median of the data.

Now in the notes it says that when , is symmetric around some which occurs when .

So its symmetrical around which if you performed the sign test on would show its the median...! Hellary I cant really explain my thoughts I have no idea how I'm gonna write this down...