Section B: The Wear IT Clothing Factory- Sewing Machine Procurement decision. (30 Marks)

Wear IT Clothing factory is currently undertaking a review of the efficiency of their sewing machines. The factory usestwo differenttypes of sewing machinesType A-at least three years old andType B-recently purchased. Theaveragemachine is supposed to use 20 Watts per day.

As the operations manager of Wear IT Clothing, you are tasked to investigate if the machines are reaching this rate of efficiency. In this case, the lessWatts a machine uses the more efficient it is and the less electricity it uses a day.

Theaimis to identify if the newly purchased machines (Machine Type B) use significantly less electricity. Using your knowledge ofpoint estimators and confidence intervalsand the guidelines below, provide a business proposal/argument for the phasing out of the old machines.

A sample has been collected as per below table:

A sample has been collected as per below table: [old machines] [new machines} 21,13 19,75 27,55 12,95 12,33 14,65 1. What is the best estimator of the population mean in this instance? {2) Construct a point estimate for the mean machine efficiency rate for both machine types (2). 2. Discuss how you came to your point estimate and what were the assumptions behind the answer (3). 3. Calculate the standard deviation of the samples for both machine types and discuss what it means in this context. {4) Would the sample standard deviation be different from the population standard deviation? Give a reason for your answer. [2) 4. Construct a 95% confidence interval for the mean machine efficiency rate for machine type A {5) 5. Construct a 95% confidence interval rate for the mean machine efficiency rate for machine type B