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Chapter 14: Q3BSC (page 654)
Control Limits In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?
The value of the lower control limit should be adjusted to 0.
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Listed below are annual sunspot numbers paired with annual high values of the Dow Jones Industrial Average (DJIA). Sunspot numbers are measures of dark spots on the sun, and the DJIA is an index that measures the value of select stocks. The data are from recent and consecutive years. Use a 0.05 significance level to test for a linear correlation between values of the DJIA and sunspot numbers. Is the result surprising?
Sunspot | DJIA |
45 | 10941 |
31 | 12464 |
46 | 14198 |
31 | 13279 |
50 | 10580 |
48 | 11625 |
56 | 12929 |
38 | 13589 |
65 | 16577 |
51 | 18054 |
Quarters. In Exercises 9鈥�12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: Run Chart Treat the 100 consecutive measurements from the 20 days as individual values and construct a run chart. What does the result suggest?
Quarters. In Exercises 9鈥�12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: Notation Find the values of \({\bf{\bar \bar x}}\)and\({\bf{\bar R}}\). Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an \({\bf{\bar x}}\) chart
Child Restraint Systems Use the numbers of defective child restraint systems given in Exercise 8. Find the mean, median, and standard deviation. What important characteristic of the sample data is missed if we explore the data using those statistics?
In Exercises 5鈥�8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.
If the R chart and\(\bar x\)chart both showed that the process of manufacturing aircraft altimeters is within statistical control, can we conclude that the altimeters satisfy the Federal Aviation Administration requirement of having errors of no more than 40 ft when tested at an altitude of 6000 ft?
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