It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10 and out of calibration if μ ≠ 10. A test is made of the hypotheses H0: μ = 10 versus H0: μ ≠ 10. Consider three possible conclusions:

(i) The scale is in calibration.

(ii) The scale is not in 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?