Houston North Hospital is trying to improve its image by providing a positive ex

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-paitent sample of the survey results over the past 7 days yielded the following data:

A. The control limits to include 99.73% of the random variation in meal satisfaction are:

UCLp= _____(enter your response as a number between 0 and 1, rounded to three decimal places).

LCLp=_____(enter your response as a number between 0 and 1, rounded to three decimal places).

No. of Unsatisfied Patients 26 Sample Size 100 100 100 100 100 100 100 Day 2 3 4 6 15 10 24 19 6

Explanation / Answer

99.73% control limit signifies a 3 control limit

Standard error (Sp) = sqrt(p_bar*(1 - p_bar)/N) = sqrt(0.1743*(1 - 0.1743)/100) = 0.0379

UCLp = p_bar + 3*Sp = 0.1743 + 3*0.0379 = 0.288
LCLp = p_bar - 3*Sp = 0.1743 - 3*0.0379 = 0.060

Day
(sample) No. of unsatisfied patients (N.p) p
= N.p/N 1 26 0.2600 2 22 0.2200 3 6 0.0600 4 15 0.1500 5 10 0.1000 6 24 0.2400 7 19 0.1900 Average (p_bar) 0.1743

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