## 6.6Optional: Confidence intervals for one proportion

(Answers are available in Sect. A.6)

The timing of pubertal maturation can vary which can have impacts upon behaviour studied

…the relationships between maturational timing and body image, school behavior, and deviance

Duncan et al. (1985), (p. 231)

Sample data were collected from

…children and youth of the entire United States drawn by the National Center for Health Statistics… known as the National Health Examination Survey (1966–1970). Data were collected on 5,735 adolescents’ physical and psychological status…

1. What type of research question is being answered: Descriptive, relational or interventional? Explain.
2. For the 2864 males in the sample, 352 were classified as maturing late. Compute the sample estimate of the population proportion of males who mature late.
3. Compute the precision of this estimate (that is, the standard error).
4. Compute an approximate 95% confidence interval for the population proportion of boys that mature late based on the sample proportion
5. Confirm that the conditions necessary for this calculation to be statistically valid are met.
6. If the researchers wished to estimate the true proportion of boys that mature late to within give-or-take 0.02 with 95% confidence, would a larger or smaller sample be needed? Explain.
7. If the researchers wished to estimate the proportion of boys maturing late within give-or-take 0.02 with 95% confidence, what size sample would be needed?

### References

Duncan, Paula Duke, Philip L. Ritter, Sanford M. Dornbusch, Ruth T. Gross, and J. Merrill Carlsmith. 1985. “The Effects of Pubertal Timing on Body Image, School Behavior, and Deviance.” Journal of Youth and Adolescence 14 (3): 227–35.