3. Steve, the manager of the accounting office of a large corporation was interesting in studying the problems of errors in the daily data entry of its clients information into the computer system. The manager selected samples of 200 account numbers from each day's output for a period of 25 days and inspected each item for errors (nonconformities). The following data was recorded.

Day errors pi Day Error pi Day Error Pi DAY ERROR pi

1 5 0.015 8 1 0.005 14 2 0.010 20 4 0.010

2 8 0.025 9 25 0.125 15 8 0.040 21 3 0.015

3 2 0.010 10 4 0.020 16 5 0.025 22 14 0.070

4 11 0.055 11 4 0.005 17 10 0.050 23 10 0.050

5 6 0.030 12 6 0.030 18 13 0.065 24 6 0.030

6 14 0.070 13 9 0.045 19 5 0.025 25 7 0.035

7 8 0.040

(NOTE:The total # of errors = 190. The average proportion of errors isp = 0.0380. The data is located in the worksheet labeledacct v21.mwx.

(i) Find the centerline and the 3-sigma limits for ap-chart. (3 pts)

LCL =_______ Centerline =________ UCL =____

(ii) Using Minitab, generate the appropriate control chart for the data located in the worksheet labeledacct v21.mwx. Determine whether the process is in control. (Be complete! Be sure to check all the rules!) (3 pts)

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(iii) Suppose it is known that during one of those days, the company experienced a computer glitch. During that day, 25 errors were recorded. Consider the computer glitch to an assignable cause and thus that day is removable. Has the removal of the assignable cause significantly improved the process? perform the appropriate test of hypothesis. (Letp1= fraction nonconforming before removal of the assignable cause andp2= fraction nonconforming after the removal of the assignable cause.) Use= 0.05. (3 pts)

NOTE:You may do question by hand or by using Minitab.

H0:____

Ha:_____

p-value =_______

or test statistic =_______

Rejection Region

Conclusion:

4. Consider a double-sampling plan withn1= 100, c1= 5, n2= 150 andc2= 8. (i) Set up the two-stages of the sampling plan. (5 pts)

Stage 1:

Stage 2:

(ii) Suppose the number of defectives found in the first sample is 6. What is your decision concerning the disposition of the lot at the end of the first stage of sampling (i.e., accept the lot, reject the lot, or take a second sample)? Justify your answer