1607 Resistance training is a popular form of conditioning a

(16.07) 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 4169 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 4169 weight-lifting injuries, 1432 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____

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.343487647          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.007354634          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.326347874          
Thus,              
Margin of error = z(alpha/2)*sp =    0.017109437          
lower bound = p^ - z(alpha/2) * sp =   0.32637821          
upper bound = p^ + z(alpha/2) * sp =    0.360597084          
              
Thus, the confidence interval is              
              
(   0.32637821   ,   0.360597084   ) [ANSWER]