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 H1: 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?

c. Assume that the scale is in calibration, but the conclusion is reached that the scale is not in calibration. Which type of error is this?

d. Assume that the scale is not in calibration. Is it possible to make a Type I error? Explain.

e. Assume that the scale is not in calibration. Is it possible to make a Type II error? Explain.