Question

(22.06) 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 4280 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 4280 weight-lifting injuries, 1456 were classified as accidental.

What is a 96% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental?

The 96% confidence interval (±±0.001) is from  to

Answer 1

Solution :

Given that,

n = 4280

x = 1456

Point estimate = sample proportion = = x / n = 1456 / 4280 = 0.340

1 - = 1 - 0.340 = 0.660

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z_/2 = Z_0.02 = 2.05

Margin0 of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.05 * (((0.340 0.660) / 4280)

= 0.015

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.340 - 0.015 < p < 0.340 + 0.015

0.325 < p < 0.355

The 96% confidence interval for the population proportion p is : (0.325 , 0.355)