The calibration of a scale is to be checked by weighing a 11 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 u denote the true average weight reading on the scale. (a) What hypotheses should be tested? OH: = 11 H₂H > 11 Ο Ηγ: μ = 11 H₂: μ = 11 O Ho: #11 H₂:μ< 11 OH₂ = 11 H₂H < 11 O Ho: 11 H₂:μ = 11 (b) with the sample mean itself as the test statistic, what is the P-value when x = 10.81? (Round your answer to four decimal places.) 2.086 What would you conclude at significance level 0.01? O Conclude that the true mean measured weight is the same as 11 kg. O Conclude that the true mean measured weight differs from 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration judged unnecessary when in fact = 10.9? (Round your answer to four decimal places.)