## Related questions with answers

**Hospital length of stay.** Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS in the United States is $4.5$ days (Healthcare Cost and Utilization Project Statistical Brief, October 2014). A random sample of 20 hospitals in one state had a mean LOS of $3.8$ days and a standard deviation of $1.2$ days. Interpret the interval in terms of this application.

Solution

VerifiedGiven:

$\begin{align*} n&=\text{Sample size}=20 \\ \overline{x}&=\text{Sample mean}=3.8 \\ s&=\text{Sample standard deviation}=1.2 \\ c&=\text{Confidence coefficient}=90\%=0.90 \end{align*}$

We need to interpret the confidence interval for the population mean.

The confidence interval for the population mean is $\overline{x}\pm E$ with the margin of error $E=E=t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}$.

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