1. The administrators of a four-year college wanted to estimate the proportion o
ID: 3218603 • Letter: 1
Question
1. The administrators of a four-year college wanted to estimate the proportion of the senior students who intended to pursue a graduate degree. In a random sample of 200 senior students, 20.5% of them indicated that they intended to pursue a graduate degree. Construct a 95% confidence interval for the corresponding true proportion.
2.In a 1999-2000 longitudinal study of youth baseball, researchers found that 29% of 295 young pitchers complained of elbow pain after pitching.
(a) Construct a 95% confidence interval for the proportion of young pitchers who may develop elbow pain after pitching.
( , ) (Carry 3 decimal digits.)
(b) A coach claims that only 1 player in 5 is at risk of arm injury from pitching. Is this claim consistent with your confidence interval?
A. Yes, because the confidence interval contains 0.20.
B. No, because the confidence interval contains 0.20.
C. No, because the confidence interval excludes 0.20.
D. Yes, because the confidence interval excludes 0.20.
Explanation / Answer
1) here p=0.205
std error =(p(1-p)/n)1/2 =0.0285
for 95% CI, z=1.96
hence confidence interval =sample proportion -/+ z*std error =01491 ; 0.2609
2) a( p=0.29
std error =0.0264
hence confidence interval =sample proportion -/+ z*std error =0.238 ; 0.342
b)C. No, because the confidence interval excludes 0.20.
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