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Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject鈥檚 intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: $\stackrel{\mathbf{炉}}{\mathbf{x}}\mathbf{=}\mathbf{2}\mathbf{.42}\mathbf{,}\mathit{s}\mathbf{=}\mathbf{2}\mathbf{.84}$.

a. Estimate $\mathit{渭}$, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of $\mathit{渭}$?

d. Compute the interval, $\stackrel{\mathbf{炉}}{\mathbf{x}}\mathbf{卤}\mathbf{2}\mathit{s}$. How does the interpretation of this interval differ from that of the confidence interval, part a?

Step by step solution

01

Given information

Sample size n=86, the mean$\stackrel{炉}{x}=2.42$ and the standard deviation s=2.84.

02

Estimating the mean μ

Here, the confidence coefficient is 0.90. Therefore,

$\begin{array}{c}\left(1鈭�伪\right)=0.90\\ 伪=0.10\\ \frac{伪}{2}=0.05\end{array}$

From table, the required$z_{0.05}$value for 90% confidence level is 1.645.

The 90% confidence interval is obtained is obtained below:

$\begin{array}{c}\stackrel{炉}{\mathrm{x}}卤{\mathrm{z}}_{\frac{\mathrm{伪}}{2}}\left({\mathrm{蟽}}_{\stackrel{炉}{\mathrm{x}}}\right)=2.42卤1.645\left(\frac{2.84}{\sqrt{86}}\right)\\ =2.42卤0.504\\ =\left(2.42+0.504,2.42鈭�00.504\right)\end{array}$

That is $\left(1.916,2.924\right)$

Thus, the 90% confidence interval for the mean intension to comply score for the population of all entry-level accounts$\left(渭\right)$ lies between 1.916 and 2.924.

03

Interpretation

There is 90% confident that the mean intention to comply score for the population of all entry-level accounts$\left(渭\right)$ lies between 1.916 and 2.924.

04

Calculating the proportion

About 90% of all similarly constructed confidence intervals will contain the true value of population mean$\left(渭\right)$ in repeated sampling.

05

Computing the confidence interval

$\begin{array}{c}\stackrel{炉}{\mathrm{x}}卤2\mathrm{s}=2.42卤2\left(2.84\right)\\ =2.42卤5.68\\ =\left(2.42+5.68,2.42鈭�5.68\right)\\ =\left(鈭�3.26,8.1\right)\end{array}$

Thus, the interval $\stackrel{炉}{\mathrm{x}}卤2\mathrm{s}$is $\left(鈭�3.26,8.1\right)$.

From, part a. the 95% confidence interval provides the range of values for the population mean $\left(渭\right)$. But, the interval$\stackrel{炉}{\mathrm{x}}卤2\mathrm{s}$ provides the range of actual values of X.

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