SOLUTION: 4. A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. One hundred participants are enrolled in the study and randomize

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Question 1152118: 4. A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. One hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. Generate a 95% CI for the difference in proportions of participants reporting a reduction of symptoms between the experimental and placebo groups.
A) (1.237, 3.232)
B) (0.114, 0.486)
C) (0.600, 0.300)
D) (1.529, 8.012)
Answer by MathLover1(20850) About Me  (Show Source):
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it given that:
n%5B1%5D=50, x%5B1%5D=30
=> p%5B1%5D=x%5B1%5D%2Fn%5B1%5D=30%2F50=0.6



n%5B2%5D=50, x%5B2%5D=15
=> p%5B2%5D=x%5B2%5D%2Fn%5B2%5D=15%2F50=0.3



The 95% confidence interval is:
CI=%28%280.6-0.3%29%2B-z%2Asqrt%280.6%281-0.6%29%2F50%2B0.3%281-0.3%29%2F50%29%29
from standard normal table, the value of z for 95% confidence level is 1.96
CI=+%280.3%2B-1.96%2Asqrt%280.009%29%29
CI=+%280.3%2B-1.96%2A0.0948683%29
CI=+%280.3%2B-0.185941868%29
CI=+0.486 or CI=+0.114

answer: B) (0.114, 0.486)