Question

Houston North Hospital is trying to improve its image by providing a positive experience for its patients and their relatives. Part of the​ "image" program involves providing​ tasty, inviting patient meals that are also healthful. A questionnaire accompanies each meal​ served, asking the​ patient, among other​ things, whether he or she is satisfied or unsatisfied with the meal. A 100​-patient sample of the survey results over the past 7 days yielded the following​ data: Day No. of Unsatisfied Patients 1 22 2 22 3 10 4 17 5 10 6 26 7 15 The control limits to include​ 99.73% of the random variation in meal satisfaction​ are: UCL=? LCL=? Based on the developed control​ limits, the number of unsatisfied patients has been: In Control or out of control?

Answer 1

Answers:

Day	Unsatisfied patients	Observations	proportion of defect= Unsatisfied patients/observations	P
1	22	100	0.220	0.1743
2	22	100	0.220	0.1743
3	10	100	0.100	0.1743
4	17	100	0.170	0.1743
5	10	100	0.100	0.1743
6	26	100	0.260	0.1743
7	15	100	0.150	0.1743
total	122	700
steps and formulas
Probability of defects=P=	total unsatisfied patients/total observations			0.1743
Q=	1-P			0.8257
N=	average sample size			100
UCL=	P + 3*squareroot(P*Q/N)			0.288
LCL=	P - 3*squareroot(P*Q/N)			0.0605
	defects cannot be negative, therefore negative LCL is taken as '0'			0.060
Standard deviation		squareroot(P*Q/N)		0.0379

• the no. of unsatisfied patients have been in control. As we can see that none of the proportion of defect lies outside the control limits.