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. A random sample of 4160 patients aged 8–30 admitted to U.S. emergency rooms with the Consumer Product Safety Commission code "weightlifting" were obtained. These injuries were further classified as "accidental" if caused by dropped weight or improper equipment use. Of the 4160 weightlifting injuries, 1560 were classified as accidental. Give a 90% confidence interval for the proportion of weightlifting injuries in this age group that were accidental. Follow the four-step process. (Round your answers to THREE decimal places.)

_____ to _____

Answer 1

Solution :

Given that,

1) Point estimate = sample proportion = = x / n = 1560 / 4160 = 0.375

1 - = 1 - 0.375 = 0.625

2) At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

3) Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.375 * 0.625) / 4160 )

= 0.012

4) A 90% confidence interval for population proportion p is ,

- E < p < + E

0.375 - 0.012 < p < 0.375 + 0.012

( 0.363 < p < 0.387 )