## Related questions with answers

The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10, 2009), researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. Use Wilson’s adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result.

Solution

VerifiedGiven:

$\begin{aligned} n&=\text{Sample size}=333 \\ x&=\text{Number of successes}=1 \\ c&=\text{Confidence level}=95\%=0.95 \end{aligned}$

Wilson's adjustment adds 2 successes and 2 failures to the sample.

The sample proportion is the number of successes divided by the sample size:

$\hat{p}=\dfrac{x+2}{n+4}=\dfrac{1+2}{333+4}=\dfrac{3}{337}\approx 0.008902$

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