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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 to a large number of IRS telephone representatives to determine the proportion of correct responses. Historically, the average proportion of correct responses has been 70 percent. Recently, IRS representatives have been receiving more training.

On April 26, the set of 25 tax questions was again asked of 20 randomly selected IRS telephone representatives. The proportions of correct answers were: 16, 20, 19, 15, 21, 19, 21, 21, 17, 21, 23, 16, 22, 19, 17, 21, 23, 16, 21, and 15.

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

- UCL = _____
- LCL = _____

(Enter your responses rounded to four decimal places. If your answer for LCL is negative, enter this value as 0.)

Answer :

The upper control limit (UCL) for the p-chart is 0.7926, and the lower control limit (LCL) is 0.4238.

To calculate the control limits for the p-chart, we need to use the formula:

UCL = p' + z * √(p'(1-p')/n)

LCL = p' - z * √(p'(1-p')/n)

Where:

p' is the average proportion of correct responses (70% or 0.70)

z is the z-score (3)

n is the sample size (20)

Calculating the control limits:

UCL = 0.70 + 3 * √(0.70(1-0.70)/20) = 0.70 + 3 * √(0.21/20) ≈ 0.7926

LCL = 0.70 - 3 * √(0.70(1-0.70)/20) = 0.70 - 3 * √(0.21/20) ≈ 0.4238

Therefore, the upper control limit (UCL) for the p-chart is approximately 0.7926, and the lower control limit (LCL) is approximately 0.4238. These control limits help identify when the proportion of correct responses deviates significantly from the average, indicating a potential improvement or deterioration in accuracy.

To learn more about upper and lower control limits, here

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