QUESTION 3 Statistical Decision Making and Quality Control Show all calculations

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QUESTION 3 Statistical Decision Making and Quality Control Show all calculations/reasoning Guide to marks: 18 marks 4 for a), 4 for a(2), 2 for b(1), 3 for b(2), 2 for b(3), 3 for b(4) (a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. In the past the mean time has been 20 hours with a standard deviation of 5 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 observations to monitor labour time. If management wishes to establish x-bar control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL 2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. Hypothesis testing Argon Advertising Agency has suggested to Specialty Store that it use mail circulars for the area within a 15 km radius of its store as its major source of advertising. Asked, "Why not extend the area beyond 15 km?" Argon's representative answered: "Your average customer lives no more than 9 km from the store, so that 15 km will cover almost all your potential customers." The owner of Specialty Store was not convinced of the truth of this answer and decided to test the statement that the average customer lives no more than 9 km from the store, sample of 50 customers was taken, and a mean travelling distance of 10.22 km was found. Based on the sample results, test the hypothesis that the average customer lives no more than 9 km from the store at a significance level of = 0.05. Experience shows that = 5 km. Your answer should respond to the following four requirements: 1. Show the null and alternative hypotheses. 2. Calculate the critical value. 3. Sketch the situation. 4. Assess the appropriate conclusion

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QUESTION 3 Statistical Decision Making and Quality Control Show all calculations/reasoning Guide to marks: 18 marks 4 for a), 4 for a(2), 2 for b(1), 3 for b(2), 2 for b(3), 3 for b(4) (a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. In the past the mean time has been 20 hours with a standard deviation of 5 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 observations to monitor labour time. If management wishes to establish x-bar control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL 2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. Hypothesis testing Argon Advertising Agency has suggested to Specialty Store that it use mail circulars for the area within a 15 km radius of its store as its major source of advertising. Asked, "Why not extend the area beyond 15 km?" Argon's representative answered: "Your average customer lives no more than 9 km from the store, so that 15 km will cover almost all your potential customers." The owner of Specialty Store was not convinced of the truth of this answer and decided to test the statement that the average customer lives no more than 9 km from the store, sample of 50 customers was taken, and a mean travelling distance of 10.22 km was found. Based on the sample results, test the hypothesis that the average customer lives no more than 9 km from the store at a significance level of = 0.05. Experience shows that = 5 km. Your answer should respond to the following four requirements: 1. Show the null and alternative hypotheses. 2. Calculate the critical value. 3. Sketch the situation. 4. Assess the appropriate conclusion

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