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 3983 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 3983 weight-lifting injuries, 1612 were classified as accidental. What is a 90% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental? The 90% confidence interval (±0.001) is from to

Answer 1

Solution :

Given that,

n = 3983

x = 1612

= x / n = 1612 / 3983 = 0.405

1 - = 1 - 0.405 = 0.595

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.405 * 0.595) / 3983) = 0.013

A 90 % confidence interval for population proportion p is ,

+/ - E

0.405 +/- 0.013

The 90% confidence interval for the population proportion p is : (0.392 ,418)