Problem 10-5 Using samples of 194 credit card statements, an auditor found the f

Question

Problem 10-5

Using samples of 194 credit card statements, an auditor found the following:
Use Table-A.

a. Determine the fraction defective in each sample. (Round your answers to 4 decimal places.)

b.If the true fraction defective for this process is unknown, what is your estimate of it? (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Estimate            ______ %

c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? (Round your intermediate calculations and final answers to 4 decimal places.)

d.What control limits would give an alpha risk of .03 for this process? (Round your intermediate calculations to 4 decimal places. Round your "z" value to 2 decimal places and other answers to 4 decimal places.)

z = _____, _____ to ______

e.What alpha risk would control limits of .0470 and .0072 provide? (Round your intermediate calculations to 4 decimal places. Round your "z" value to 2 decimal places and "alpha risk" value to 4 decimal places.)

z = _____, alpha risk = _____

f.Using control limits of .0470 and .0072, is the process in control? YES/ NO

no

yes

g.Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? (Round your intermediate calculations and final answers to 2 decimal places.)

h.Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? YES/ NO

Yes

No

Explanation / Answer

a.
Fraction Defective = Number of errors/samples
Fraction Defective of sample 1 = 3/194 = 0.0514
Fraction Defective of sample 2 = 2/194 = 0.0103
Fraction Defective of sample 3 = 5/194 = 0.0257
Fraction Defective of sample 4 = 11/194 = 0.0567

b.

Total Number of samples is 4

Estimate= (0.0514+0.0103+0.0257+0.0567)/4 = 0.1441/4 = 0.036 or 3.6%

c.

Std. Deviation= root((0.036)(1-0.036)/194)
= root(0.03470/194)
= root 0.000178
= 0.01334

Mean = (0.0514+0.0103+0.0257+0.0567)/4 = 0.036

d.

Service Probability= 1-(0.03/2)= 0.985
Z= 2.17

Mean= 0.036, Z= 2.17 and Std. deviation= 0.0133
Control Limits= 0.036+-(2.17*0.0133)
= 0.0072 to 0.0648

So z = 2.17, 0.0072 to 0.0648

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