Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study,auditors were asked to make judgmentS about the frequency of errors to be found in an audit. The judgments by the auditors were then compared to the actual results.Suppose the following data were obtained from a similar study; lower scores indicate better judgments. If answer is zero enter "0".DirectIndirectCombination18.017.815.617.819.216.314.017.021.420.219.124.319.120.324.524.820.927.026.725.023.9SourceSum ofDegrees Mean SquareFp-valueofSquaresof(to 2(to 2(to 2Variation(to 2 decimals)Freedomdecimals)decimals)decimals)TreatmentsErrorTotalUse a = 0.05 to test to see whether the basis for the judgment affects the quality of the judgment.The p-value is - Select your answer -What is your conclusion?Select your answer -

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Description: Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study,auditors were asked to make judgmentS about the frequency of errors to be found

Given Information: Direct Indirect Combination 18.0 17.0 24.5 17.8 21.4 24.8 15.6 20.2 20.9…

Answered: Auditors must make judgments about…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 13PT

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Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study,
auditors were asked to make judgmentS about the frequency of errors to be found in an audit. The judgments by the auditors were then compared to the actual results.
Suppose the following data were obtained from a similar study; lower scores indicate better judgments. If answer is zero enter "0".
Direct
Indirect
Combination
18.0
17.8
15.6
17.8
19.2
16.3
14.0
17.0
21.4
20.2
19.1
24.3
19.1
20.3
24.5
24.8
20.9
27.0
26.7
25.0
23.9
Source
Sum of
Degrees Mean Square
F
p-value
of
Squares
of
(to 2
(to 2
(to 2
Variation
(to 2 decimals)
Freedom
decimals)
decimals)
decimals)
Treatments
Error
Total
Use a = 0.05 to test to see whether the basis for the judgment affects the quality of the judgment.
The p-value is - Select your answer -
What is your conclusion?
Select your answer -

Expert Solution

Step 1

Given Information:

Direct	Indirect	Combination
18.0	17.0	24.5
17.8	21.4	24.8
15.6	20.2	20.9
17.8	19.1	27.0
19.2	24.3	26.7
16.3	19.1	25.0
14.0	20.3	23.9

First take the total of all individual values and call it as $T$

$T$ = 432.9 and $n$ = 21

Hence, the correction factor is:

$\frac{T^{2}}{n} = \frac{{(432.9)}^{2}}{21} = 8923.924286$

Step 2

Total Sum of squares is calculated as follows:

$\begin{array}{rcl} T S S & = & \sum_{i} {x_{i j}}^{2} - \frac{T^{2}}{n} \\ = & {(18.0)}^{2} + {(17.8)}^{2} + {(15.6)}^{2} + . . . . . . . {(25.0)}^{2} + {(23.9)}^{2} - 8923.924286 \\ = & 9208.77 - 8923.924286 \\ = & 284.845714 \end{array}$

SS between is calculated as follows:

$\begin{array}{rcl} S S b e t w e e n & = & \sum_{i} \frac{{(T_{j})}^{2}}{n_{j}} - \frac{{(T)}^{2}}{n} \\ = & (\frac{118.7 \times 118.7}{7}) + (\frac{141.4 \times 141.4}{7}) + (\frac{172.8 \times 172.8}{7}) - 8923.924286 \\ = & 2012.812857 + 2856.28 + 4265.691429 - 8923.924286 \\ = & 9134.784286 - 8923.924286 \\ = & 210.86 \end{array}$

SS within is calculated as follows:

$\begin{array}{rcl} S S w i t h i n & = & \sum_{i} {x_{i j}}^{2} - \sum_{j} \frac{{T_{j}}^{2}}{n_{j}} \\ = & 9208.77 - 9134.784286 \\ = & 73.985714 \\ \approx & 73.99 \end{array}$

Degrees of freedom for between samples is obtained as:

$\begin{array}{rcl} d f & = & k - 1 \\ = & 3 - 1 \\ = & 2 \end{array}$

Degrees of freedom within samples:

$\begin{array}{rcl} d f & = & n - k \\ = & 21 - 3 \\ = & 18 \end{array}$

Total degrees of freedom:

$\begin{array}{rcl} d f & = & n - 1 \\ = & 21 - 1 \\ = & 20 \end{array}$

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