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

2525

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

7171

percent.​ Recently, IRS representatives have been receiving more training. On April​ 26, the set of

2525

tax questions were again asked of 20 randomly selected IRS telephone representatives. The proportions of correct answers​ were:

1515​,

1616​,

1919​,

1616​,

1515​,

1414​,

2121​,

2121​,

1717​,

2121​,

2323​,

1616​,

2222​,

1515​,

1515​,

2020​,

2323​,

1616​,

2121​,

and

1515.

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

33.

The

UCL Subscript pUCLp

equals

nothing

and the

LCL Subscript pLCLp

equals

nothing.

​(Enter your responses rounded to four decimal places. If your answer for

LCL Subscript pLCLp

is​ negative, enter this value as

0.​)

Answer 1

UCL=P bar+ Factor

LCL=Pbar-Factor

UCL =1.050

and LCL=0.589

P bar=total defective answers/total sum of n or 25

1	B	C	D
2	Sample	defective answers	P or Proportion of correct answers
3	25	21.25	15%
4	25	21	16%
5	25	20.25	19%
6	25	21	16%
7	25	21.25	15%
8	25	21.5	14%
9	25	19.75	21%
10	25	19.75	21%
11	25	20.75	17%
12	25	19.75	21%
13	25	19.25	23%
14	25	21	16%
15	25	19.5	22%
16	25	21.25	15%
17	25	21.25	15%
18	25	20	20%
19	25	19.25	23%
20	25	21	16%
21	25	19.75	21%
22	25	21.25	15%
23	P bar	0.8195
24	Factor calculation	0.231
25	UCL	1.050
26	LCL	0.589

Formula:

1	B	C	D
2	Sample	defective answers	P or Proportion of correct answers
3	25	=(25*(1-D3))	0.15
4	25	=(25*(1-D4))	0.16
5	25	=(25*(1-D5))	0.19
6	25	=(25*(1-D6))	0.16
7	25	=(25*(1-D7))	0.15
8	25	=(25*(1-D8))	0.14
9	25	=(25*(1-D9))	0.21
10	25	=(25*(1-D10))	0.21
11	25	=(25*(1-D11))	0.17
12	25	=(25*(1-D12))	0.21
13	25	=(25*(1-D13))	0.23
14	25	=(25*(1-D14))	0.16
15	25	=(25*(1-D15))	0.22
16	25	=(25*(1-D16))	0.15
17	25	=(25*(1-D17))	0.15
18	25	=(25*(1-D18))	0.2
19	25	=(25*(1-D19))	0.23
20	25	=(25*(1-D20))	0.16
21	25	=(25*(1-D21))	0.21
22	25	=(25*(1-D22))	0.15
23	P bar	=SUM(C3:C22)/SUM(B3:B22)
24	Factor calculation	=3*(SQRT(((1-C23)*C23)/25))
25	UCL	=C23+C24
26	LCL	=C23-C24