I get stuck in the following question:
You set up a two-sided hypothesis test for a population mean μ with a null hypothesis of: μ=100. You chose a significance level of α=0.05. The p-value calculated from the data is 0.12, and hence you failed to reject the null hypothesis. Suppose that after your analysis was completed and published, an expert informed you that the true value of μ is 104. How would you describe the result of your analysis?
I wonder if there might be no error? The true mean is around that in the null hypothesis, then I thought there would be no error. I mean if the true value of μ is 100.000001, the error would be the same as when it is 104. But there should be a buffer for the null hypothesis.
Any suggestions would be highly appreciated.