(a) State the appropriate null and alternative hypotheses.
(b) 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!
(c) Repeat Part (b) for a Type II error.
(d) 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 sample mean X; (ii) in terms of the z-statistic; and (iii) in terms of the p-value.
(e) The test is conducted (using n = 50) and the result is 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?
Now refer back to the original scenario, and suppose that we’re back at the test design stage so the appropriate sample size has not yet been determined and consequently no data has been obtained. Continue to assume a known standard deviation of σ = 25.
(a) An increase of 10 units per day in the line’s average production rate is considered to be very important. What sample size should be used if the test is to have an 80% chance of detecting such an increase? A 90% chance? a 95% chance?
(b) Suppose that we decide to base the test on a sample of size n = 50. Calculate the power of the test at μ = 800.01 and for μ-values ranging from 802.5 to 825 in increments of 2.5. Report your results in a table. Then create a pretty power function plot (power in the vertical axis vs. μ in the horizontal axis)."
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