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 MEALS 42 SAMPLE SIZE 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 December 1 December 2 47 63 December 3 December 4 December 5 December 6 48 60 62 43 62 December 7 December 8 December 9 66 December 10 53 [s23)] 10,000 a. Determine the p, Sp, UCL and LCL based on the questionnaire results, using a confidence interval of 95.5 percent, which is two standard deviations. (Round your answers to 4 decimal places.) .0546 Sp UCL LCL

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can you help me find sp, UCL, LCL 

**Analysis of Hospital Meal Quality Survey**

As a newly appointed assistant administrator at a local hospital, your initial project involves assessing the quality of meals offered by the food-service department. A 10-day survey was conducted, where a questionnaire was distributed to 400 patients after each meal. The patients were required to indicate whether their meal was satisfactory or unsatisfactory. For simplification, assume 1,000 questionnaires were returned out of 1,200 meals served daily. The results are summarized below:

**Survey 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**     |                                | **10,000**  |

**Statistical Analysis:**

The analysis aims to determine critical parameters: \( \bar{p} \), \( S_p \), UCL, and LCL, using a confidence interval of 95.5%, equivalent to two standard deviations.

- **Mean Proportion (\( \bar{p} \)):** Calculated and given as 0.0546.
- **Standard Deviation (\( S_p \)):** Not provided; calculation needed.
- **Upper Control Limit (UCL):** Not provided; calculation needed.
- **Lower Control Limit (LCL):** Not provided; calculation needed.

**Instructions:**

1. Calculate \( S_p \), UCL, and LCL from the questionnaire data.
2. Apply a confidence interval of 95.5%, which uses two standard deviations.
3. Round your answers to four decimal places.
Transcribed Image Text:**Analysis of Hospital Meal Quality Survey** As a newly appointed assistant administrator at a local hospital, your initial project involves assessing the quality of meals offered by the food-service department. A 10-day survey was conducted, where a questionnaire was distributed to 400 patients after each meal. The patients were required to indicate whether their meal was satisfactory or unsatisfactory. For simplification, assume 1,000 questionnaires were returned out of 1,200 meals served daily. The results are summarized below: **Survey 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** | | **10,000** | **Statistical Analysis:** The analysis aims to determine critical parameters: \( \bar{p} \), \( S_p \), UCL, and LCL, using a confidence interval of 95.5%, equivalent to two standard deviations. - **Mean Proportion (\( \bar{p} \)):** Calculated and given as 0.0546. - **Standard Deviation (\( S_p \)):** Not provided; calculation needed. - **Upper Control Limit (UCL):** Not provided; calculation needed. - **Lower Control Limit (LCL):** Not provided; calculation needed. **Instructions:** 1. Calculate \( S_p \), UCL, and LCL from the questionnaire data. 2. Apply a confidence interval of 95.5%, which uses two standard deviations. 3. Round your answers to four decimal places.
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