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 72 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 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?

use 3-σ control limits; base your interpretation of the results of the current study using a control chart analysis with the control chart UCL and LCL based on the information from the historical data

Answer 1

Answer:

Calculate the proportion of each observation by

p% = Correct response / Sample size

Number of Observations	Correct response	Sample size	Proportion p (%)
1	18	25	0.720
2	16	25	0.640
3	19	25	0.760
4	21	25	0.840
5	20	25	0.800
6	16	25	0.640
7	21	25	0.840
8	16	25	0.640
9	17	25	0.680
10	10	25	0.400
11	25	25	1.000
12	18	25	0.720
13	25	25	1.000
14	16	25	0.640
15	20	25	0.800
16	15	25	0.600
17	23	25	0.920
18	19	25	0.760
19	21	25	0.840
20	19	25	0.760
Average of all observations (p bar)	0.750

z = 3

p bar = 0.750

Sample size (n) = 25

Standard Deviation (σ) = √[p bar * (1- p bar)]/n = 0.0866

UCL = p bar+zσ = 0.750+(3*0.0866) = 1.0098

LCL = p bar-zσ =   0.750-(3*0.0866) = 0.4902

Data for plotting p-Chart:

p-Chart

Since the proportion (p) is crossing the LCL, the tax information process is NOT in statistical control.

Since z = 3, it is using 3σ control limit (i.e. +-3σ).

Based on the above calculations the process is NOT in statistical control.