You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. You conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. For simplicity in this problem, assume that the response was 1,000 returned questionnaires from the 1,200 meals each day. The results are as follows: NUMBER OF UNSATISFACTORY SAMPLE MEALS SIZE 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 10,000 December 1 42 December 2 December 3 December 4 47 63 December 5 December 6 December 7 48 60 62 43 December 8 62 December 9 66 December 10 53 [s23)]

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**Quality Assessment of Patient Meals in a Hospital**

As a newly appointed assistant administrator at a local hospital, your task is to evaluate the quality of the meals provided by the food-service department. A 10-day survey was conducted where 400 patients were asked to report if their meals were satisfactory or unsatisfactory. For simplicity, it is assumed that 1,000 responses were received daily out of the 1,200 meals served. Here are the results:

| Date       | Number of Unsatisfactory Meals | Sample Size |
|------------|-------------------------------|-------------|
| December 1 | 42                            | 1,000       |
| December 2 | 47                            | 1,000       |
| December 3 | 63                            | 1,000       |
| December 4 | 48                            | 1,000       |
| December 5 | 60                            | 1,000       |
| December 6 | 62                            | 1,000       |
| December 7 | 43                            | 1,000       |
| December 8 | 62                            | 1,000       |
| December 9 | 66                            | 1,000       |
| December 10| 53                            | 1,000       |

**Total Sample Size Over 10 Days: 10,000**

**Objective:**
a. Calculate the proportion of unsatisfactory meals (\(\overline{p}\)), the standard deviation of the proportion (\(S_p\)), and the Upper Control Limit (UCL) and Lower Control Limit (LCL) using a 95.5% confidence interval, equivalent to two standard deviations. The answers should be rounded to four decimal places.

---

**Calculation Table:**

| Metric | Value |
|--------|-------|
| \(\overline{p}\) |        |
| \(S_p\)          |        |
| UCL              |        |
| LCL              |        | 

Note: The calculations for \(\overline{p}\), \(S_p\), UCL, and LCL will help determine the quality control measures for the hospital food-service department, providing insight into where improvements might be necessary.
Transcribed Image Text:**Quality Assessment of Patient Meals in a Hospital** As a newly appointed assistant administrator at a local hospital, your task is to evaluate the quality of the meals provided by the food-service department. A 10-day survey was conducted where 400 patients were asked to report if their meals were satisfactory or unsatisfactory. For simplicity, it is assumed that 1,000 responses were received daily out of the 1,200 meals served. Here are the results: | Date | Number of Unsatisfactory Meals | Sample Size | |------------|-------------------------------|-------------| | December 1 | 42 | 1,000 | | December 2 | 47 | 1,000 | | December 3 | 63 | 1,000 | | December 4 | 48 | 1,000 | | December 5 | 60 | 1,000 | | December 6 | 62 | 1,000 | | December 7 | 43 | 1,000 | | December 8 | 62 | 1,000 | | December 9 | 66 | 1,000 | | December 10| 53 | 1,000 | **Total Sample Size Over 10 Days: 10,000** **Objective:** a. Calculate the proportion of unsatisfactory meals (\(\overline{p}\)), the standard deviation of the proportion (\(S_p\)), and the Upper Control Limit (UCL) and Lower Control Limit (LCL) using a 95.5% confidence interval, equivalent to two standard deviations. The answers should be rounded to four decimal places. --- **Calculation Table:** | Metric | Value | |--------|-------| | \(\overline{p}\) | | | \(S_p\) | | | UCL | | | LCL | | Note: The calculations for \(\overline{p}\), \(S_p\), UCL, and LCL will help determine the quality control measures for the hospital food-service department, providing insight into where improvements might be necessary.
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