Question

In a study of youth​ baseball, researchers found that 24​% of 260 randomly selected young pitchers complained of elbow pain after pitching. ​a) Create a 95​% confidence interval for the percentage of young pitchers who may develop elbow pain after pitching. ​b) A coach claims that only about 1 player in 5 is at risk of arm injury from pitching. Is this claim consistent with your confidence​ interval?

Answer 1

a)

sample proportion, = 0.24
sample size, n = 260
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.24 * (1 - 0.24)/260) = 0.0265

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0265
ME = 0.052

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.24 - 1.96 * 0.0265 , 0.24 + 1.96 * 0.0265)
CI = (0.1881 , 0.2919)

b)

This is not consistent because confidence interval contains 0.20