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 m 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  = 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 = 10.1? When μ = 9.8?