## 6.5 Confidence intervals for one proportion

Endotracheal intubation (ETI) is a method for maintaining an open airway or as a method for administering certain drugs for ill patients.

ETI is widely used for airway management of children in the out-of-hospital setting, but for many years little evidence was available on the effect of using ETI.

A study examined the use of ETI for airway management of children in the out-of-hospital setting (Gausche et al. 2000).

- For the
**BVM sample**, 123 out of the 404 patients survived. For those receiving BVM, compute the sample*odds*of a patient who survived. - For the
**BVM sample**, 123 out of the 404 patients survived. For those receiving BVM, compute an estimate of the population*proportion*of patients who survive. - Explain the difference between the meaning of the two above calculations.
- In another sample of 404 patients who received the BVM treatment,
would we expect to find
*exactly*123 surviving? Why or why not? - Compute the
*standard error*, which indicates the sampling variability in the estimate of \(p\). Explain what is meant by the term 'sampling variation' in this context. - Every time a new sample is chosen, the sample will likely yield a different value for \(\hat{p}\). Sketch the distribution that shows how much the value of \(\hat{p}\) is likely to change from one sample to the next.
- Compute an approximate 95% confidence interval for the population proportion based on the sample proportion.
- Write a sentence communicating this confidence interval.
- Confirm that the conditions necessary for this calculation to be statistically valid are met.
- If the researchers wished to estimate the true survival proportion to within give-or-take 0.01 with 95% confidence, would a larger or smaller sample be needed? Explain.
- If the researchers wished to estimate the true survival proportion to within give-or-take 0.01 with 95% confidence, estimate the size sample that would be needed.
- For the ETI sample, 110 out of 416 patients survived. Use this information to construct a two-way table of treatment against survival.
- Select a graphical summary that could be used to display the information. Sketch this display.
- From this table,
compute the odds ratio of a BVM patient
*not*surviving compared to an ETI patient*not*surviving. Interpret this value. - What did you learn about using ETI on children? Would you prefer to recommend ETI or BVM on children? What other information would you need to help make your decision?

### References

Gausche M, Lewis RJ, Stratton SJ, Haynes BE, Gunter CS, Goodrich SM, et al. Effect of out-of-hospital pediatric endotracheal intubation on survival and neurological outcome: A controlled clinical trial. Journal of the American Medical Association. 2000;283(6):783–90.