Question 5 (of 7 value: 0.71 oints Problem 10-6 A medical facility does MRis for

Question

Question 5 (of 7 value: 0.71 oints Problem 10-6 A medical facility does MRis for sports injuries. Occasionally a test yields incondlusive results and must be repeated. Use the following sample data and n-200 SAMPLE 23 4 56 789 10 11 12 13 Number of retests1 2 2 0 2 1 2 02 7 3 2 1 a. Determine the upper and lower control imits for the fraction of retests using two-sigma limits. (Do not round intermediate calculations. Round your final answers to 4 decimal places. Leave no cells blank -be certain to enter "" wherever required.) UCL LCL b. Is the process in control? Yes No Hints References eBook & Resources Hint#1 2

Explanation / Answer

p-bar = Total number of retest/Total number of observation = (1+2+2+0+2+1+2+0+2+7+3+2+1)/(200*13) = 0.0096

n = 200

s = sqrt(p-bar*(1-p-bar)/n) = sqrt(0.0096*(1-0.0096)/200) = 0.0069

UCL = p-bar + z*s

LCL = p-bar - z*s

For 2 sigma, z = 2

a) UCL = 0.0096 + 2*0.0069 = 0.0234

LCL = 0.0096 - 2*0.0069 = -0.0042. Hence 0.0000

b) Retest ratio for sample with highest retest is Sample 10 = 7/200 = 0.035

As the value is higher than UCL. Process is not in control

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