Note : the Answer should be Computerized The IRS is concerned with improving the

Question

Note : the Answer should be Computerized

The IRS is concerned with improving the accuracy of tax information given by its representatives over the telephone. Previous studies involved asking a set of 25 questions ofa large number of IRS telephone representatives to determine the proportion of correct responses. Historically, the aver- age proportion of correct responses has been 72 percent Recently, IRS representatives have been recelving more training. On April 26, the set of 25 tax questions were again asked of 20 randomly selected IRS telephone representatives The numbers of correct answers were 18, 16, 19,21, 20, 16, 21, 16, 17, 10,25, 18, 25, 16, 20, 15, 23, 19,21, and 19. What are the upper and lower control limits for the appropriate p-chart for the IRS? Use z 3. Is the tax information process in statistical control? a. b.

Explanation / Answer

Thus p bar = total no. of incorrect answers/total no. of answers

= 125/(20*25)

= 125/500

= 0.25

The next step is to determine the standard deviation. Standard deviation = (p bar*(1- p bar)/n)^0.5

= (0.25*(1-0.25)/25)^0.5

= 0.0866

A.UCL of the p chart = p bar+z*standard deviation = 0.25+(3*0.0866) = 0.50981

LCL = p bar-z*standard deviation = 0.25-(3*0.0866) = -0.00981

B. No, the information process is not in statistcal control. For the 10th sample representative p bar = 15/25 = 0.60. This is above the UCL of 0.50981.

Sample represnetatives Total no. of questions No. of correct answers No. of incorrect answers 1 25 18 7 2 25 16 9 3 25 19 6 4 25 21 4 5 25 20 5 6 25 16 9 7 25 21 4 8 25 16 9 9 25 17 8 10 25 10 15 11 25 25 0 12 25 18 7 13 25 25 0 14 25 16 9 15 25 20 5 16 25 15 10 17 25 23 2 18 25 19 6 19 25 21 4 20 25 19 6 Total no. of incorrect answers 125

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