The calibration of a scale is to be checked by weighing a 14 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 = 0.200 kg. Let denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: = 14 H: > 14 Ho: = 14 Ha 14 H = 14 Ha: < 14 Ho: = 14 Ha < 14 (b) With the sample mean itself as the test statistic, what is the P-value when x = 13.81? (Round your answer to four decimal places.) A What would you conclude at significance level 0.01? O Conclude that the true mean measured weight differs from 14 kg. Conclude that the true mean measured weight is the same as 14 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact = 14.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact = 13.9? (Round your answer to four decimal places.)