I'm getting a bit confused about paired and unpaired data, for example in this question I don't understand how this data is paired.
If it was the same steel pipes that were left uncoated first in the soil to see the effects of corrosion and then taken out and were coated this time and then left in the soil to see the effects of corrosion then I understand the data would have been paired because the definition of paired data that I know is when there is one sample which has been tested twice (repeated measures) but here clearly it is different steel pipes that are left uncoated and coated so how is this data paired.
So when deciding that data is paired or not what exactly are we supposed to look at?
Also can I quickly check: null hypothesis would be: mean1-mean2=0, alternative hypothesis would be mean1-mean2>0, where mean 1 is for uncoated pipes and mean 2 is for coated pipes and our rejection region would be (using a t-statistic) t>t(alpha) , where alpha is 5%
The concept of paired data does not imply that the items are the same. You have to use the paired t–test when there is one measurement variable and two categorical variables, and one of the categorical variables has only two values (i.e., you have multiple pairs of observations). In your case the measurement variable is the corrosion level, and the categorical variables are location and coated/uncoated status.