Question: The supplied Minitab Worksheet Bars.MTW contains data on the weights (g) from trial production runs of the NUE chocolate bars on each of three different lines at the Napbisco factory.

1. Given that the data are in time order, create run charts and state whether or not there is any evidence of special cause variation for any of the lines. (Marks 10)
2. Display the data for all three lines in the form of boxplots on one chart. Add reference lines to the display corresponding to the customer specification limits of 61.0 and 62.5 for bar weight and explain why it is not surprising that it was decided not to use Line 1 for any commercial production runs. (Marks 15)
3. Obtain the means and standard deviations of the sample of bar weights from Lines 2 and 3. (Marks 5)
4. Use normal probability plots to demonstrate that it is reasonable to model the distribution of bar weight for Lines 2 and 3 using normal distributions. (Marks 5)
5. Use the View Probability facility, under Graph > Probability Distribution Plot, to estimate the proportion of non-conforming bars, with respect to weight, for both Lines 1 and 2. State steps that could possibly be taken in order to increase these proportions. (Marks 15)
6. Test formally whether or not there is any evidence of a difference between location and variability for Lines 1 and 2. (Marks 10)
7. The production manager had a hunch that Line 2 produced more non-conforming bars than Line 3, in terms of characteristics other than weight. During a production run in which Lines 2 and 3 ran in parallel. 240 bars from each were inspected for nonconformities i.e. the numbers of bars that were broken, misshapen, inadequately coated etc. were recorded. The counts were 17 and 8 respectively. Do these data support the manager’s hunch? (Marks 5)

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