The calibration of a scale is to be checked by 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 = .200 kg. let µ denote the true average weight reading on the scale. (a) what hypotheses should be tested? (b) with the sample mean itself as the test statistic, what is the p-value when x = 9.85, and what would you conclude at significance level .01? (c) for a test with α = .01, what is the probability that recalibration is judged unnecessary when in fact µ = 10.2?