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?

Answer:a:  That the mean weight of the trials is 10 kgb:  See attached photo for workStep-by-step explanation:We want to see if the scale is weighing properly and are using a 10 kg weight to calibrate it.  That means our hypothesis test is that the mean weight of the trails (in this case 25) is 10 kg.The hypothesis we will use areH0:  µ = 10Ha:  µ ≠ 10The alternate hypothesis has a not equals to sign because if the scale weighs too much or to little, then it needs to be better calibrated, so it's a two tailed test.