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 3933 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 3933 weight-lifting injuries, 1648 were classified as accidental.

What is a 98% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental?

The 98% confidence interval (±±0.001) is from  to

Answer 1

Solution :

Given that,

n = 3933

x = 1648

Point estimate = sample proportion = = x / n = 1648 / 3933 = 0.419

1 - = 1 - 0.419 = 0.581

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= 2.326 * (((0.419 * 0.581) / 3933)

= 0.018

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.419 - 0.018 < p < 0.419 + 0.018

0.401 < p < 0.437

The 98% confidence interval for the population proportion p is : (0.401 , 0.437)