7.8 Optional: CI for one proportion

This question is optional; e.g., if you need more practice, or you are studying for the exam.

(Answers are available in Sect. A.6)

This question has a video solution in the online book, so you can hear and see the solution.

The timing of pubertal maturation can vary, which can have impacts upon behaviour. One research project 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...

What type of research question is being answered: descriptive, relational, repeated-measures of correlational? Explain.
For the \(2,864\) males in the sample, \(352\) were classified as maturing late. Compute the sample estimate of the population proportion of males who mature late.
Compute the precision of this estimate (that is, the standard error).
Compute an approximate \(95\)% confidence interval for the population proportion of boys that mature late based on the sample proportion.
Confirm that the conditions necessary for this calculation to be statistically valid are met.
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.
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 PD, Ritter PL, Dornbusch SM, Gross RT, Carlsmith JM. The effects of pubertal timing on body image, school behavior, and deviance. Journal of Youth and Adolescence. 1985;14(3):227–35.