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In: Statistics and Probability

Because of high production change-over time and costs, a director of manufacturing must convince management that...

Because of high production change-over time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of £320 per hour. A sample of 1,000 products have been analysed using the innovative manufacturing method. The director of manufacturing observed the mean cost was £300 per hour and a standard deviation of £20 per hour. a) Define an appropriate system of hypotheses (null hypothesis and alternative hypothesis) to test whether the mean cost of production is reduced. (b) What assumption(s) about the population is/are necessary to perform this test? ( c) What is the value of the test statistic? ( d) What is the approximate p-value associated to the test statistic? (e) What is the critical value? f) At the 1% significance level, what is your conclusion? If the level of significance was 5% would your conclusion be different? Explain your answer. (g) Calculate the 95% approximate confidence interval for the population mean cost of production.

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