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 4094 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 4094 weight-lifting injuries, 1681 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 = 4094

x = 1681

Point estimate = sample proportion = = x / n = 1681/4094 = 0.411

1 - = 1 - 0.411 = 0.589

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z_/2 = 1.960

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

= 1.960 * ((0.411*(0.589) /4094 )

= 0.015

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.411- 0.015 < p < 0.411+ 0.015

0.396< p < 0.426

The 95% confidence interval for the population proportion p is : 0.396< p < 0.426