Question

The calibration of a scale is to be checked be weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with σ = .2kg. Let µ denote the true average weight reading on the scale. (a) What hypotheses should be tested? (b) Suppose the scale is to recalibrated if either ¯y ≥ 10.1032 or ¯y ≤ 9.8968. What is the probability that recalibration is carried out when it is actually unnecessary? (c) What is the probability that recalibration is judged unnecessary when in fact µ = 10.1? When µ = 9.8? (d) Let z = y¯−10 σ/√ n . For what value c is the rejection region in part (c) equivalent to the two-tailed rejection region: either z ≥ c or z ≤ −c? (e) If the sample size were only 10 rather than 25, how should the procedure in part (e) be altered so that α = 0.05? (f) Using the test of part (e), what would you conclude from the following sample data: 9.981, 10.006, 9.857, 10.107, 9.888, 9.793, 9.728, 10.439, 10.214, 10.19 (g) Reexpress the test procedure of part (b) in terms of the standardized test statistic Z = Y¯ −10 σ/√ n

Answer 1