In: Statistics and Probability
In a 1993 article in Accounting and Business Research, Meier, Alam, and Pearson studied auditor lobbying on several proposed U.S. accounting standards that affect banks and savings and loan associations. As part of this study, the authors investigated auditors’ positions regarding proposed changes in accounting standards that would increase client firms’ reported earnings. It was hypothesized that auditors would favor such proposed changes because their clients’ managers would receive higher compensation (salary, bonuses, and so on) when client earnings were reported to be higher. The following table summarizes auditor and client positions (in favor or opposed) regarding proposed changes in accounting standards that would increase client firms’ reported earnings. Here the auditor and client positions are cross-classified versus the size of the client firm.
You will need to type in the FOUR pieces of data into Minitab, along with column headings LARGE and SMALL (firms). Data go into the white cells in Minitab, starting with row 1. Column headings go in the grey shaded cells in Minitab. Do not type in the totals, as those are not new pieces of data.
a) Auditor Positions
Large Firms |
Small Firms |
Total | |
In Favor | 19 | 124 | 143 |
Opposed | 10 | 24 | 34 |
Total | 29 | 148 | 177 |
Client Positions
Large Firms |
Small Firms |
Total | |
In Favor | 26 | 106 | 132 |
Opposed | 20 | 25 | 45 |
Total | 46 | 131 | 177 |
(a) Test to determine whether auditor positions
regarding earnings-increasing changes in accounting standards
depend on the size of the client firm. Use α = .05. (Round
your expected frequencies to 2 decimal places. Round your answer to
3 decimal places.)
x^2 = ; so (Click to select) Reject Do not reject H0: independence for auditor positions regarding earnings-increasing changes.
(b) Test to determine whether client positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your answer to 3 decimal places.)
x^2 = ; so (Click to select) Do not reject Reject H0: independence for client positions regarding earnings-increasing changes.
(d) Does the relationship between position and the
size of the client firm seem to be similar for both auditors and
clients?
Yes
No
(a) Test to determine whether auditor positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your expected frequencies to 2 decimal places. Round your answer to 3 decimal places.)
Col 1 | Col 2 | Total | ||
Row 1 | Observed | 19 | 124 | 143 |
Expected | 23.43 | 119.57 | 143.00 | |
O - E | -4.43 | 4.43 | 0.00 | |
(O - E)² / E | 0.84 | 0.16 | 1.00 | |
Row 2 | Observed | 10 | 24 | 34 |
Expected | 5.57 | 28.43 | 34.00 | |
O - E | 4.43 | -4.43 | 0.00 | |
(O - E)² / E | 3.52 | 0.69 | 4.21 | |
Total | Observed | 29 | 148 | 177 |
Expected | 29.00 | 148.00 | 177.00 | |
O - E | 0.00 | 0.00 | 0.00 | |
(O - E)² / E | 4.36 | 0.85 | 5.21 | |
5.214 | chi-square | |||
1 | df | |||
.0224 | p-value |
x^2 = 5.214; so Reject H0: independence for auditor positions regarding earnings-increasing changes.
(b) Test to determine whether client positions regarding earnings-increasing changes in accounting standards depend on the size of the client firm. Use α = .05. (Round your answer to 3 decimal places.)
Col 1 | Col 2 | Total | ||
Row 1 | Observed | 26 | 106 | 132 |
Expected | 34.31 | 97.69 | 132.00 | |
O - E | -8.31 | 8.31 | 0.00 | |
(O - E)² / E | 2.01 | 0.71 | 2.72 | |
Row 2 | Observed | 20 | 25 | 45 |
Expected | 11.69 | 33.31 | 45.00 | |
O - E | 8.31 | -8.31 | 0.00 | |
(O - E)² / E | 5.90 | 2.07 | 7.97 | |
Total | Observed | 46 | 131 | 177 |
Expected | 46.00 | 131.00 | 177.00 | |
O - E | 0.00 | 0.00 | 0.00 | |
(O - E)² / E | 7.91 | 2.78 | 10.69 | |
10.685 | chi-square | |||
1 | df | |||
.0011 | p-value |
x^2 = 10.685 ; so Reject H0: independence for client positions regarding earnings-increasing changes.
(d) Does the relationship between position and the
size of the client firm seem to be similar for both auditors and
clients?
Yes