Question: In its current configuration, an assembly line produces an average of μ = 800 personal computers per day with standard deviation σ = 25 computers. A newly hired production engineer believes that by switching from a "push" assembly line approach to a "pull" (JIT) approach, the process can be speeded up with no compromise in quality of assembly. To test this belief, an experimental assembly line is set up for n days using the pull approach, and we observe the number of computers produced each day. Assume that the standard deviation for the experimental line is the same as for the existing line, and that the number of computers produced per day is approximately normally distributed. The question under study is whether the results from the experiment provide strong evidence that the new approach increases daily output.

1. State the appropriate null and alternative hypotheses.
2. What are the implications , to the firm, of making a Type I error in this hypothesis testing situation? Don’t just repeat the definition of a Type I error. Tell me a (short) story!
3. Repeat Part (b) for a Type II error.
4. Suppose that the Type I error probability is specified as α = 0.05, and that the sample size is n = 50. State the decision rule for testing the hypothesis that you specified in Part (a) (i) in terms of the z -statistic; (ii) in terms of the sample mean \(\bar{X}\) ; and (iii) in terms of the p -value.
5. The test is conducted (using n = 50) and the result is \(\bar{X}\) = 804 units. Report the test conclusion. Show the numbers/logic used to reach this conclusion and interpret it in the context of the problem. Should the company switch to the ‘pull’ system? X

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