SOLUTION: In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the New York half marathon, and found that 13% of t

Question 140268: In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the New York half marathon, and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two week period. What would be the null hypothesis? Find a 90% confidence interval for the percentage of New York half marathon runners who got sick in the two weeks after the race.

PLS pls help, I am only a student in long distance education and need help to solve exam problems. This is from my question paper
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the New York half marathon, and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two week period. What would be the null hypothesis? Find a 90% confidence interval for the percentage of New York half marathon runners who got sick in the two weeks after the race.
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1st sample:
n1=400
p-hat = 0.13
----------------
2nd sample:
n2=400
p-hat = 0.03
----------------
Ho: p1 - p2 = 0
---------------
Confidence Interval
p1-hat - p2-hat = 0.10
E = 1.645*sqrt[(0.13*0.87/400) + (0.03*0.97)/400)] = 0.031016
90% CI: 0.1-0.031016 < p < 0.1 + 0.31016
= 0.68984 < p < 1.31016
===============
Cheers,
Stan H.

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