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In hypothesis testing the concept of type 1 and type 2 error is very important and very often we come across the graph shown below. I have trouble understanding why is the curve for alternative hypothesis shifted compared to the null hypothsis? graph

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    $\begingroup$ If my anwser was sufficient to your question, please mark it as a solution :) $\endgroup$ Apr 8, 2020 at 6:27

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The idea is that the population has the mean of the null hypotesis, say mean height of Sweden is 181cm. Then you do a sample of the population and find that the sample height is 185. Is this enough for you to discard the null and accept the alternative?

This is what the curves are trying to illustrate. The reason for the shifted curve for the alternative is that the mean is located at a different point on the x-axis (185 in my example).

So, given that h0 is true (mean 181), what are the probability to draw a sample mean of 185? That would be the right tail of the null curve straight under the alternatives mean and all to the right of it.

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