Problem 10-5 Using samples of 198 credit card statements, an auditor found the f

Question

Problem 10-5

Using samples of 198 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 .0136 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 .0136, is the process in control?

yes

no

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

Sample 1 2 3 4 Number with errors 5 4 7 8

Explanation / Answer

Please find answers to first 4 questions :

SAMPLE

FRACTION DEFECTIVE

1

5/198 = 0.0252

2

4/198 = 0.0202

3

7/198 = 0.0353

4

8/198 = 0.0404

B) Estimated fraction defective of the process , Pbar

= Total number with errors / ( Number of samples x Sample size )

= ( 5 + 4 + 7 + 8 ) / ( 4 x 198 )

= 24 /( 4 x 198 )

= 0.0303

C) Given sample size = n = 198

Estimate of mean for fraction defective = pbar = 0.0303

Estimate of standard deviation for fraction defection , Sd

= Square root ( Pbar x ( 1 – Pbar) / n )

= Square root ( 0.0303 x 0.9697/198 )

= 0.0122

D) service probability corresponding to alpha risk of 0.03

= 1 – ( 0.03/2 )

= 0.985

Z value corresponding to service probability of 0.985 = NORMSINV ( 0.985 ) = 2.17

SAMPLE

FRACTION DEFECTIVE

1

5/198 = 0.0252

2

4/198 = 0.0202

3

7/198 = 0.0353

4

8/198 = 0.0404

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.