The IRS is concerned with improving the accuracy of tax information given by its
ID: 343335 • Letter: T
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 71 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 number of correct answers were:
21, 16, 19, 8, 21, 21, 21, 16, 17, 16, 22, 8, 24, 19, 19, 16, 23, 15, 21, and 16.
To determine he upper and lower control limits for an appropriate p-chart for the IRS, with z = 4, data is entered into OM Explorer as shown below.
a. The entry of defect data is correct.
True
False
b. The entry of the sample size is correct.
True
False
c The entry of the standard deviation for control limits is correct.
True
False
PLEASE INDICATE CORRECT ANSWER!
columhs 0.8975 Compute p-Bar 20 10 Sample size p-Bar * Enter p-Bar manually 2 12 13 Defects in Sample 21 26 16 27 19 28 8 29 21 30 21 31 21 32 16 33 17 34 16 35 22 36 8 37 24 38 19 39 19 40 16 41 23 42 15 43 21 44 16 45 46 47 48 49 50 sigma * Enter sigma manually Std. Dev. For CL's 0.067820996 Compute sigma 1.33 17 18 Upper Control Limit Lower Control Limit 0 0.9877 0.8073 20 21 23 24 25 26 27 28 29 30 31 32 12 13 15 16 17 19 20 21 35 36 37 38 23 24 25Explanation / Answer
Defect data in a sample will be :
Defect data = 25 ( sample size ) – Number of correct answers
Therefore ,
Defect data in sample 1 = 25 – 21 = 4
Defect data in sample 2 = 25 – 16 = 9
Defect data in sample 3 = 25 – 19 = 6 ….so on and so forth
Therefore , entry of defect data is FALSE
Sample size = 25 ( not 20. 2o is the number of samples )
Presented below is the table for number of defects for 20 samples :
Sample No
Correct answer
Defects
1
21
4
2
16
9
3
19
6
4
8
17
5
21
4
6
21
4
7
21
4
8
16
9
9
17
8
10
16
9
11
22
3
12
8
17
13
24
1
14
19
6
15
19
6
16
16
9
17
23
2
18
15
10
19
21
4
20
16
9
Sum of total number of defects in 20 samples = 141
Number of samples = n = 20
Alternately p bar = Sum of defects / ( Sample size of 25 x 20 as number of samples )
= 141 /500 = 0.282
Therefore standard deviation of control limits in p chart
= Square root ( pbar x ( 1 – pbar)/n)
= Square root ( 0.282 x 0.718/25)
= 0.0899
C. THE ENTRY FOR STANDARD DEVIATION FOR CONTROL LIMITS IS CORRECT: FALSE
- THE ENTRY OF DEFECT DATA IS CORRECT : FALSE
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