The IRS is concerned with improving the accuracy of tax information given by its

Question

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 of a large number of IRS telephone representatives to determine the proportion of correct responses. Historically, the average proportion of correct responses has been 75 percent. Recently, IRS representatives have been receiving more training. On April 26, the set of 25 tax questions were again asked of 20 randomly selected IRS telephone representatives. The proportions of correct answers were: 19,20,19,20,15,15,21,21,17,21,23,16,24,19,21,20,23,16,21, and 15.

a. What are the upper and lower control limits for the appropriate p-chart for the IRS? Use z = 3.

b. Is the tax information process in statistical control?

Explanation / Answer

a)

The points 8, 10, and 20 are below the lower control limits. So the process is out of control

0.9794

(b) yes the tax information process is in statistical control

p Chart Summary Intermediate Calculations Sum of Subgroup Sizes 500 Number of Subgroups Taken 20 Average Sample/Subgroup Size 25 Average Proportion of Nonconforming Items 0.706 Three Standard Deviations 0.2734 Preliminary Lower Control Limit 0.4326 p Chart Control Limits Lower Control Limit 0.4326 Center 0.7060 Upper Control Limit

0.9794

(b) yes the tax information process is in statistical control

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