It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10. A test...

It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10. A test is made of the hypotheses H₀: μ = 10 versus H₁: μ ≠ 10. Consider three possible conclusions: (i) The scale is in calibration. (ii) The scale is out of calibration. (iii) The scale might be in calibration. a) Which of the three conclusions is best if H₀
is rejected? b) Which of the three conclusions is best if H₀
is not rejected? c) Is it possible to perform a hypothesis test in a way that makes it possible to demonstrate conclusively that the scale is in calibration? Explain.