Question: o determine whether the process is in statistical control, you would compare the actual proportion of defective items in each sample to the calculated control

o determine whether the process is in statistical control, you would compare the actual proportion of defective items in each sample to the calculated control limits (UCL and LCL) on the p-chart. Here's how you can make the assessment:
Plot the Data: Plot the sample proportions (p-hat) for each of the 10 samples on the p-chart.
Add Control Limits: Plot the UCL and LCL lines on the chart. In your case, UCL is approximately 0.0402, and LCL is approximately 0.0018.
Analyze the Chart:
If all data points (sample proportions) fall within the control limits, the process is considered to be in statistical control. This means that the observed variations are likely due to common causes, and the process is stable.
If any data point falls above the UCL or below the LCL, it indicates an out-of-control situation. This suggests that there may be special causes of variation at work, and you should investigate and take corrective actions to understand and eliminate those special causes.
So, by examining the p-chart with your given data and control limits, you can make the assessment. If all 10 sample proportions are within the control limits, then the process is in statistical control. If any sample proportion falls outside the control limits, you indicate that there are special causes of variation, and further investigation is needed.

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