What is going on in this problem?

#1
There is an example attached, and I don't know how the answer was gotten. The formula that was used doesn't make any sense to me. Can anyone please explain what happened in the problem? Thanks.
 
#2
Hi,

i can be wrong but i know sign test like that. I havent understood your formula but you can understand test's sense from below.

Also , you can look this link for more information:
http://caspar.bgsu.edu/~courses/Stats/Lectures/Lect_SignTest.html
Also ,ask it to uncle google. Just write "sign test".

firstly,

17-20= -3 (-)
15-20=-5 (-)
...
...
...
24-20=4 (+)

we sum (-) ones.
we sum (+) ones.
we dont sum datas , we only sum (-) and (+) signs.

In your data , i can see 3 negatives and 7 positives. We choose minumum one so we will work with negatives.

And than , we look sign test table,
We should look k= 3 and n=12.

Our table value = 0.073

alfa=0.05 , table value > alfa ; so we accept Ho hypothesis.

Signt test table,
 
#3
The formula refers to the binomial distributions. Remember most of statistical inference is essentially proof by contradiction. In the null you assume what you want to contradict and start reasoning from there. Though I note that we lay out how we will do so before observing the data to avoid reasoning that is essentially multiple testing in disguise. As you can see though from this example people often do hand waving in that department. If they stick to "known" test quite often they decide how they will test after they see the data. Strictly speaking that is "bad". Anyway back to the point.

If the null is that the median is 20 what is the probability that the next observation is over the median? Under the median? Theres a .50 probability that observations are over or under the median for any unknown distribution. Its part of the definition of median. If you observe more observations over your hypothesised median than not you start to gather evidence to contradict that the median is what you assumed under the null.

The actual formulas are just the binomial distribution formulas.
 
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