1.2

You may need to use the appropriate technology to answer this question. A production line operation is tested for lling weight accuracy using the following hypotheses. Hypothesis Conclusion and Action HO: ,u = 16 Filling okay; keep running. Ha: u s 16 Filling off standard; stop and adjust machine. The sample size is 30 and the population standard deviation is J = 0.7. Use or = 0.05. (a) What would a type II error mean in this situation? 0 Rejecting H0 and letting the process continue to run when actually over-lling or under-lling exists. 0 Rejecting H0 and stopping the process when actually no over-filling or under-lling exists. 0 Accepting HO and letting the process continue to run when actually overfilling or underfilling exists. 0 Accepting HD and stopping the process when actually no overfilling or underfilling exists. (b) What is the probability of making a type [I error when the machine is overlling by 0.6 ounces? (Round your answer to four decimal places.) l:l (c) What is the power of the statistical test when the machine is overfilling by 0.6 ounces? (Round your answer to four decimal places.) :l (d) Show the power curve for this hypothesis test. 1.0 1.0 1.0 0.8 0.8 0.8 5:, 0.6 5:, 0.6 5;, 0.6 E 0.4 E 0.4 E 0.4 0.2 0.2 0.2 0.0 , __, , __, , ,__l, 0.0 , __, , , , ,__l, 0.0 , __, , ,__l, ,__I, 15.4 15.6 15.8 16.0 16.2 16.4 16.6 15.4 15.6 15.8 16.0 16.2 16.4 16.6 15.4 15.6 15.8 16.0 16.2 16.4 16.6 Possible values of p Possible values of p Possible values of p O (90 @ 1.0 0.8 5:, 0.6 E 0.4 0.2 0.0 15.4 15.6 15.8 16.0 16.2 16.4 16.6 Possible values of p What information does it contain for the production manager? 0 The power curve shows the probability of rejecting HD for various possible values of p. In particular it shows the probability of not stopping and adjusting the machine under a variety of underlling and overlling situations. 0 The power curve shows the probability of not rejecting H0 for various possible values of n. In particular it shows the probability of stopping and adjusting the machine under a variety of underlling and overlling situations. 0 The power curve shows the probability of not rejecting H0 for various possible values of n. In particular it shows the probability of not stopping and adjusting the machine under a variety of underlling and overlling situations. 0 The power curve shows the probability of rejecting H0 for various possible values of p. In particular it shows the probability of stopping and adjusting the machine under a variety of underfilling and overlling situations