You are the newly appointed assistant administrator at a local hospital, and you

Question

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: a. Determine the P, S_p, UCL and LCL based on the questionnaire results, using a confidence interval of, 95.5 percent, which is two standard deviations. b. What comments can you make about the process? The process is in statistical control. The process is out of statistical control.

Explanation / Answer

Date   Unsatisfactory Meal   Sample Size  
1-Dec   36   1000  
2-Dec   61   1000  
3-Dec   36   1000  
4-Dec   36   1000  
5-Dec   48   1000  
6-Dec   58   1000  
7-Dec   38   1000  
8-Dec   59   1000  
9-Dec   48   1000  
10-Dec   60   1000  
total = 480      
          

a)
P   = 480/(10*1000) = 0.048  
SP   = SQRT((0.048*(1-0.048))/(1000)) = 0.006759882  
UCL   = p + 1.96sp =    0.061249368 [95.5% of the area under a normal curve lies within roughly 1.96 standard deviations of the mean]
LCL   = p - 1.96 sp = 0.034750632 [95.5% of the area under a normal curve lies within roughly 1.96 standard deviations of the mean]

b)

When we see the the Tabular column data, for sample and unsatisfactory meal reports, we can see that the values if plotted on graph (1 , 36/1000) , (2 , 61/1000)... (10, 60/1000) [Since the number of days are 10 we can easily analyze data without graph]

We can see that all values are within UCL and LCL (i.e. between 0.034750632 and 0.061249368)

All values hence respects confidence level of 95.5% hence the process is under statistical control

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