Budget lapsing at army hospitals. Budget lapsing occurs when unspent funds do not carry over from one budgeting period to the next. Refer to the Journal of Management Accounting Research (Vol. 19, 2007) study on budget lapsing at U.S. Army hospitals, Exercise 2.113 (p. 126). Because budget lapsing often leads to a spike in expenditures at the end of the fiscal year, the researchers recorded expenses per full-time equivalent employee for each in a sample of 1,751 army hospitals. The sample yielded the following summary statistics:$\overline{x}=\backslash (6,563$ and $s=\backslash )2,484$. Estimate the mean expenses per full-time equivalent employee of all U.S. Army hospitals using a 90% confidence interval. Interpret the result.

The researchers recorded expenses per full-time equivalent employee for each in a sample of 1,751 army hospitals. The sample yielded the following summary statistics: $\overline{x}=\$6,563$and$s=\$2,484$.

Assume that the distribution of expenses per full-time equivalent employee is normally distributed.

Here, the confidence coefficient is 0.90.

Therefore,

$\begin{array}{rcl}\left(1-\alpha \right)& =& 0.90\\ \alpha & =& 0.10\\ \frac{\alpha }{2}& =& 0.05\\ & & \end{array}$

From table, the required value for 90% coefficient level is 1.645.

The 90% coefficient interval is obtained below:

$\begin{array}{rcl}\overline{x}+z_{\frac{\alpha }{2}}\left(\frac{\sigma }{\sqrt{n}}\right)& =& 6563\pm 1.645\times \left(\frac{2484}{\sqrt{1751}}\right)\\ & =& 6563\pm 97.65\\ & =& \left(6563-97.65,6563+97.65\right)\\ & =& \left(6465.35,6660.65\right)\\ & & \end{array}$

Therefore, the 90% confidence interval is ($6565.35, $6660.65).

There is 90% confident that the true mean expense per full-time equivalent employee of all U.S. Army hospitals$\left(\mu \right)$ lies between $6565.35 and $6660.65.