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Each day, the waste water treatment plant at a factory monitors the treated water for a variety of contaminants. The contaminant of focus here is measured in parts per billion (ppb) with a threshold of 15 ppb. Twenty five consecutive days of testing of five samples per day are shown in Table 1.
- Using the all of the data, find trial control limits for a sample mean control chart, construct the chart, and plot the data. Discuss whether the process is in statistical control.
- Using the all of the data, find trial control limits for a standard deviation control chart, construct the chart, and plot the data. Discuss whether the process is in statistical control.
- If the sample mean for each group is plotted in sequence and a simple linear regression line fitted to it, the resulting regression coefficient for slope may indicate whether there is a systematic drift in the process. Find that slope and conduct a hypothesis test at the 0.05 significance level to determine whether there is sufficient evidence that the slope is not zero.
| Group |
Set 1 |
| x1 |
x2 |
x3 |
x4 |
x5 |
| 1 |
11.04 |
13.14 |
13.10 |
16.79 |
12.56 |
| 2 |
13.53 |
9.56 |
15.06 |
10.04 |
7.75 |
| 3 |
17.29 |
15.55 |
14.35 |
17.99 |
13.86 |
| 4 |
13.73 |
19.85 |
14.70 |
17.48 |
11.25 |
| 5 |
14.28 |
10.36 |
15.39 |
12.16 |
14.05 |
| 6 |
15.85 |
12.88 |
14.22 |
10.30 |
12.30 |
| 7 |
14.69 |
7.48 |
15.77 |
11.38 |
19.52 |
| 8 |
13.06 |
15.00 |
16.06 |
8.68 |
11.94 |
| 9 |
15.62 |
14.08 |
13.32 |
15.38 |
13.12 |
| 10 |
11.79 |
8.11 |
11.31 |
9.88 |
17.22 |
| 11 |
10.88 |
12.80 |
8.44 |
10.63 |
9.98 |
| 12 |
12.70 |
13.90 |
14.83 |
13.88 |
18.27 |
| 13 |
10.73 |
11.36 |
11.91 |
6.34 |
12.65 |
| 14 |
15.91 |
7.40 |
14.64 |
15.58 |
8.18 |
| 15 |
16.95 |
9.80 |
13.39 |
9.85 |
14.91 |
| 16 |
7.76 |
6.25 |
13.46 |
16.33 |
14.72 |
| 17 |
12.68 |
11.89 |
7.84 |
12.57 |
10.13 |
| 18 |
15.06 |
16.27 |
13.21 |
12.64 |
10.34 |
| 19 |
14.64 |
8.20 |
13.86 |
15.67 |
6.98 |
| 20 |
14.45 |
14.44 |
14.38 |
16.21 |
13.34 |
| 21 |
11.50 |
15.20 |
13.31 |
8.70 |
17.42 |
| 22 |
15.26 |
11.86 |
11.81 |
15.56 |
9.85 |
| 23 |
12.71 |
12.51 |
10.42 |
9.57 |
15.36 |
| 24 |
15.11 |
8.44 |
9.07 |
11.18 |
16.73 |
| 25 |
10.49 |
15.89 |
14.54 |
15.15 |
13.66 |
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