Question

You have just set up a customer satisfaction monitoring system for your new restaurant. Each week you ask 20 randomly selected customers to respond to a simple questionnaire. One question asks, “Are you satisfied with the quality of service in this restaurant?” You have been conducting this study for the last 10 weeks and calculate that 93% of the customers have responded “yes” to your question. Set up a p-chart with two standard deviation control limits so you can determine if there has been a change in the perceived quality of your service. What are the control limits for a chart that controls the “percentage of dissatisfied customers”? (Select the closest answer. Note that your answer may differ slightly due to rounding error.)
A. .24                   -.10

B. .24                   .0

C. .12                   .01

D. .18                   .0

E. .18                   -.04

Answer 1

ANSWER: D. .18                   .0

p-chart is used for monitoring proportion defective.

In this case, it is given that 93% of the customers have responded "yes" to the question of satisfaction. In case of service, dissatisfaction is considered as a defect.

Therefore, average proportion defective, p̅ = 1 - 0.93

= 0.07

Sample size, n = 20

Standard deviation, σ_p = √(p̅(1-p̅)/n)

= sqrt(0.07*(1-0.07)/20)

= 0.057

2 sigma control limits:

UCL = p̅ + 2*σ_p = 0.07+2*0.057 = 0.18 (rounded-off)

LCL = p̅ - 2*σ_p = 0.07-2*0.057 = -0.04 ~ 0  (if the calculated value is negative, then LCL is considered as 0)

ANSWER: UCL = 0.18 , LCL = 0