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 ifH0 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.