Janice? Sanders, CEO of Pine Crest Medical? Clinic, is concerned over the number

Question

Janice? Sanders, CEO of Pine Crest Medical? Clinic, is concerned over the number of times patients must wait more than 30 minutes beyond their scheduled appointments. She asked her assistant to take random samples of 60 patients to see how many in each sample had to wait more than 30 minutes. Each instance is considered a defect in the clinic process. The table below contains the data for 15 samples.

a. Assuming Janice Sanders is willing to use? three-sigma control? limits, construct the upper and lower control limits.

The UCLp equals ______ and the LCLp equals _______. (Enter your responses rounded to four decimal places. If your answer for LCLp is? negative, enter this value as 0.?)

Explanation / Answer

p (bar) = total number of defects/total sample

Total number of defects = sum of all defects for sample 1 to sample 15 = 2+4+2+3.....+4 = 72

Total sample = 15*60 = 900 (15 samples with each sample having 60 patients)

Thus p (bar) = 72/900 = 0.08

Now, UCLp = p(bar) + z*[(p(bar*(1-p(bar))/n]^1/2

now as the control limit is three sigma, z = 3 and n = 60

Thus UCLp = 0.08+ 3*[(0.08*0.92)/60]^1/2

= 0.08+0.0980

= 0.1780. This is the UCLp

LCLp = p(bar) - z*[(p(bar*(1-p(bar))/n]^1/2

= 0.08- 3*[(0.08*0.92)/60]^1/2

= 0.08 - 0.0980

= -0.018. Since this is negative LCL will be considred as 0.

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