Heartland Hospital is trying to improve its image by providing a positive experi

Question

Heartland 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 150-patient sample of the survey results over the past 7 days yielded the following data:

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).

B. Based on the developed control limits, the number of unsatisfied patients has been: (select one)

-In control

-Out of control

Day No. of Unsatisfied Patients 22 22 Sample Size 150 150 150 150 150 150 150 y or on 13 12 26 19

Explanation / Answer

A.

99.73% control limit signifies a 3 control limit

Standard error (Sp) = sqrt(p_bar*(1 - p_bar)/N) = sqrt(0.1143*(1 - 0.1143)/150) = 0.0260

UCLp = p_bar + 3*Sp = 0.1143 + 3*0.0260= 0.192
LCLp = p_bar - 3*Sp = 0.1143 - 3*0.0260 = 0.036

B.

In control - because all the 7 values of 'p' are within the range of [0.036, 0.192]

Day
(sample) No. of unsatisfied patients (N.p) Sample size
(N) p
= N.p/N 1 22 150 0.1467 2 22 150 0.1467 3 6 150 0.0400 4 13 150 0.0867 5 12 150 0.0800 6 26 150 0.1733 7 19 150 0.1267 Average (p_bar) 0.1143

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