Let us say I make a claim that the eyesight number of corona infected patient increases.
So how should I approach this problem?
I take 1000 normal people(with normal eyesight) randomly from a population and calculate the mean and std dev of eyesight number lets say ‘d1’ and ‘sigma’.
Now I take some random 100 people from this 1000 people and infect them with corona virus.
Now this 100 people is my sample. And then I calculate the mean eyesight number from this sample denoted by d2.
So can I assume the population mean to be ‘d1’ and pop std dev = ‘sigma’ and sample mean to be ‘d2’ and then perform z-test?
Please tell me whether this approach is right or wrong and also suggest other approaches too.