# Answered Essay: Sample Number with errors 12 34 4 3 6 9 a. Determine the fraction defective in each sample. (Round your answers to 4 decimal places.) Sample Fraction defective b. If the true fraction defective for this proce

Problem 10-5 Using samples of 196 credit card statements, an auditor found the following Use Table-A Sample Number with errors 12 34 4 3 6 9 a. Determine the fraction defective in each sample. (Round your answers to 4 decimal places.) Sample Fraction defective b. If the true fraction defective for this process is unknown, what is your estimate of it? (Enter your answer as a percentage rounded to 1 decimal place. Omit the”%” sign in your resp onse.) Estimate

a) Fraction defective in each sample

 Sample Fraction Defective Calculation 1 0.0204 =4/196 2 0.0153 =3/196 3 0.0306 =6/196 4 0.0459 =9/196

b) Estimate of true fraction defective of the process = (0.0204+0.0153+0.0306+0.0459)/4 = 0.0281

c)

Mean, p = 0.0281

Standard deviation, s = SQRT(p*(1-p)/n) = 0.0118

d)

For alpha of 0.03, z = NORMSINV(1-0.03/2) = 2.17

Upper limit = p + z*s = 0.0281 + 2.17*0.0118 = 0.0537

Lower limit = p – z*s = 0.0281 – 2.17*0.0118 = 0.0025

e)

z = (0.0281-0.0092)/0.0118 = 1.60   (or z = (0.0470-0.0281)/0.0118 = 1.60)

alpha risk = 2*(1-NORMSDIST(1.6) = 0.1096

f) Yes, the process is in control, as all the fraction defective values lie within the control limits.

g)

Mean = 2 % = 0.02

Standard deviation = SQRT(0.02*(1-0.02)/196) = 0.01

h) Control chart is following:

No, the process is not in control.

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