Question

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. The data are contained in the Excel Online file below. Suppose the data were obtained from a similar study; lower scores indicate better judgments.
Direct Indirect Combination
17.0 16.6 25.2
18.5 22.2 24.0
15.8 20.5 21.5
18.2 18.3 26.8
20.2 24.2 27.5
16.0 19.8 25.8
13.3 21.2 24.2
Construct a spreadsheet to answer the following questions. Open spreadsheet Use to test to see whether the basis for the judgment affects the quality of the judgment. The -value is (to 2 decimals) . The exact -value is (to 4 decimals) .
What is your conclusion?

Answer 1

Solution :

         Direct          Indirect           Combination

1          17                  16.6                    25.2

2        18.5                22.2                    24

3        15.8                20.5                    21.5

4        18.2              18.3                       26.8

5        20.2             24.2                      27.5

6        16                   19.8                     25.8

7        13.3                21.2                      24.2

n         7                     7                           7

$\bar X$        17                   20.4                      25

s         2.238            2.501                      2.002

$\bar X_{avg}$   20.8              

Source               df           SS              MS                F          P-value

treatments        2        225.680     112.840      22.1593    0.000

error                  18        91.660       5.092

total                   20       317.340

The test hypothesis is :

$H_0$ : the basis for the judgement does not affects the quality of the judgment.

$H_a$ : the basis for the judgement affects the quality of the judgement.

Given a = 0.05, since the p-value is less than 0.05, so we reject $H_0$.

Therefore, the basis for the judgement affects the quality of the judgement.