A textile manufacturer has a large order for a cloth meant for making uniforms. The cloth is dyed using four different dyeing lines, which produce approximately equal amounts of cloth each day.

Usually not more than one line is used for one product, because no matter how well the process is controlled, differences will always appear in the shade of the dye from one line to another. But because the volume of the order is large, four lines are being used.

The shade is kept as uniform as possible by minimizing the variance of the brightness of the shade on all cloth produced. Lately, the customer has been complaining about too much variance in the brightness. It was decided to conduct an ANOVA test of the brightness of the cloth from the four lines. Random samples were taken from each line and were measured for brightness. The measurement is on a 0 to 100 scale. The sample data are:

Line 1 Line 2 Line 3 Line 4

1 66.55 66.16 68.36 72.32

2 71.91 65.94 66.81 66.69

3 67.61 68.62 66.50 72.36

4 66.13 63.86 65.22 70.88

5 71.31 69.38 65.06 69.76

6 68.99 64.55 65.42 71.05

7 71.83 66.82 66.50 68.78

8 68.99 65.56 64.82 74.40

9 69.81 63.66 68.31 66.73

10 72.49 64.71 68.17 73.58

11 69.99 67.32 65.50 66.72

12 73.44 71.39 70.39 70.37

13 70.39 63.78 75.72

14 68.42 70.25 74.65

15 71.66

16 65.14

1. Conduct the test at the 5% significance level, and report your conclusion.
2. Which pairs of lines have significant differences in their average brightness?
3. Stopping a line to adjust its average brightness is costly. If only one line can be stopped and adjusted, which one should it be? To what average brightness value should it be adjusted to minimize the variance in all the cloth produced?
4. If two lines can be stopped and adjusted, which ones should be? To what average brightness value should they be adjusted to minimize the total variance in all cloth produced?

Price: $10.67

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