9.1

You may need to use the appropriate technology to answer this question. A production line operation is tested for filling weight accuracy using the following hypotheses. Hypothesis Conclusion and Action HO: ,u = 16 Filling okay; keep running. Ha: p a 16 Filling off standard; stop and adjust machine. The sample size is 30 and the population standard deviation is o = 0.7. Use a = 0.05. (a) What would a type 11 error mean in this situation? 0 Accepting H0 and letting the process continue to run when actually overlling or underlling exists. O Accepting H0 and stopping the process when actually no over-lling or under-lling exists. O 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. (b) What is the probability of making a type II error when the machine is overlling by 0.5 ounces? (Round your answer to four decimal places.) :l (c) What is the power of the statistical test when the machine is overfilling by 0.5 ounces? (Round your answer to four decimal places.) :1 (d) Show the power curve for this hypothesis test. 1.0 1.0 1.0 0.8 0.8 0.6 0.61 0.6 Power Power Power 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 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 u Possible values of u Possible values of O i 1.0/ 0.8 0.6 Power 0.4 0.2 0.0 15.4 15.6 15.8 16.0 16.2 16.4 16.6 Possible values of u OWhat information does it contain for the production manager? 0 The power curve shows the probability of rejecting H0 for various possible values of - In particular it shows the probability of not stopping and adjusting the machine under a variety of under-filling and overfilling situations. 0 The power curve shows the probability of not rejecting H0 for various possible values of u. In particular it shows the probability of not stopping and adjusting the machine under a variety of underfilling and overlling situations. 0 The power curve shows the probability of rejecting H0 for various possible values of in. In particular it shows the probability of stopping and adjusting the machine under a variety of underlling and overfilling situations. 0 The power curve shows the probability of not 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 overfilling situations