Question

Resistance training is a popular form of conditioning aimed at enhancing sports performance and is widely used among high school, college, and professional athletes, although its use for younger athletes is controversial. Researchers obtained a random sample of 3919 patients between the ages of 8 and 30 who were admitted to U. S. emergency rooms with injuries classified by the Consumer Product Safety Commission code "weight-lifting." These injuries were further classified as " accidental" if caused by dropped weight or improper equipment use. Of the 3919 weight-lifting injuries, 1590 were classified as accidental.

What is a 95% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental?

The 95% confidence interval (±±0.001) is from__ to __

Answer 1

Solution :

Given that,

n = 3919

x = 1590

= x / n = 1590/3919 = 0.406

1 - = 1 - 0.406 = 0.594

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * [ * (1 - ) / n]

= 1.96 * [(0.406 * 0.594) / 3919]

= 0.015

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.406 - 0.015 < p < 0.406 + 0.015

0.391 < p < 0.421

The 95% confidence interval is from 0.391 to 0.421