The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose the results of different weighings are independent of one another and that the weight of each trial is normally distributed with a = .200 kg. Let U denote the true average weight reading on the scale

a What Hypothesis should be tested (state the null and alternate hypothesis?

b. Suppose the scale is to be recalibrated if either the average (X bar) is >= 10.1032 or Xbar <=9.8968. What is the probability that the recalibration is carried out when it is actually unnecessary?

c. What is the probability that the recalibration is judged unnecessary when in fact = 10.1? When = 9.8?

d. Using the data (shown to the left) as sample data, how does this compare to the hypothesis stated in part a? Test at the = .05 level

Data:

9.981

10.006

9.857

10.107

9.888

9.728

10.439

10.214

10.19

9.793

Please, show step by step.

Thank you