1 [19] GA2 (19 theory in engineering problems). a) Prepare a pie chart showing the different quality cost categories (Internal, external, appraisal and prevention costs) and percentages for the Impressive Printing Company, whose data is as shown in the table below. (15) Hint: First put the cost elements into the correct quality cost category, then find the total costs, and percentages of costs for each category. b) Comment on the results in part (a). (4) Impressive Printing Company quality costs Cost Element Quality costs Customer complaint remakes R 24 300 Printing plate revisions 25 200 Quality improvement projects 11 700 Gauging 90 000 Other waste 34 200 Correction of typographical errors 189 000 Proof reading 405 000 Quality planning 50 400 Press downtime 256 500 Bindery waste 45 900 Checking and inspection 37 800 QUESTION 2 [21] GA2 (24.5 calculations). From the data for Bollyman Theatrical Products in the table below: (a) Construct a histogram. (12.5) Note: Show the table of cell intervals and frequencies. Set up your bins or cell intervals of 0.01 units; starting with the smallest cell interval of 21.97 21.98 units, 21.98 21.99 units, until all the recorded data is contained. (b) Estimate the process capability (Cp). (10) (c) Comment on the capability of the process, from your answer in part (b). (2) Data for Bollyman Theatrical Products 22.03 21.99 22.01 21.99 22.00 22.00 22.01 22.00 22.00 22.01 22.02 22.01 22.01 22.00 21.99 21.99 21.99 22.00 22.01 22.00 22.01 22.01 22.01 22.00 22.01 22.00 22.01 22.00 21.99 22.01 21.99 22.00 22.00 22.00 22.01 22.00 22.00 21.99 22.00 22.02 22.01 21.99 22.01 21.97 22.00 22.01 22.00 21.99 22.01 22.00 21.99 22.00 22.00 22.01 21.98 22.02 22.00 22.00 22.01 22.00 22.02 22.00 22.00 22.00 22.00 22.00 22.00 22.00 22.00 22.01 22.00 22.01 22.00 22.01 22.00 22.00 21.99 22.00 22.00 22.00 22.00 22.00 22.00 22.00 22.01 21.99 22.00 22.01 22.01 22.01 22.02 22.01 22.00 21.99 22.02 22.01 21.99 22.00 22.00 22.01 QUESTION 3 [17] GA2 (17 Interpretation of data). Moir recently launched a new-flavoured pudding. The marketing manager now wants to assess the products success in the marketplace. If average sales per week are less than R5 500 per outlet, the product will be withdrawn. The results from a sample of 18 supermarket outlets countrywide showed that average sales per week were R5 275, with a sample standard deviation of R788. Assume weekly sales are normally distributed. Advise the new marketing manager if the new pudding flavour should be withdrawn or not? (a) Formulate the null and alternative hypothesis. (4) (b) Perform a hypothesis test for a single mean at the 10% level of significance. (9) (c) What statistical and management conclusions can be drawn? (4) QUESTION 4 [62] GA2 (52 calculations). One hundred insurance claim forms are inspected daily at Full Life Insurance Co. over 25 working days, and the number of forms with errors have been recorded in the table below. Sample Number 1 2 3 4 5 6 7 8 9 10 11 12 13 Number of forms with errors 3 3 3 2 0 3 0 1 7 3 2 0 0 Sample size 100 100 100 100 100 100 100 100 100 100 100 100 100 Sample Number 14 15 16 17 18 19 20 21 22 23 24 25 Number of forms with errors 4 1 2 4 0 1 1 0 2 8 1 4 Sample size 100 100 100 100 100 100 100 100 100 100 100 100 a) Construct a p-chart. (32) b) If any points occur outside the control limits, assume that assignable causes have been determined. Then construct a revised chart. (20)