In a trial of 167 patients who received 10 mg doses of a drug daily, 35 reported
ID: 3125768 • Letter: I
Question
In a trial of 167 patients who received 10 mg doses of a drug daily, 35 reported headache as a side effect. a) obtain a point estimate for the population proportion of patients who received 10 mg of a drug daily and reported head ache as a side effect. b) Verify that the requirements for constructing a confidence interval about p are satisfied. c) Construct a 99% confidence interval for the population proportion of patients who receive the drug and report headache as a side effect. d)Interpret the confidence interval
Explanation / Answer
a)
Note that
p^ = point estimate of the population proportion = x / n = 35/167 = 0.209580838 [ANSWER]
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b)
n and p^ msut satisfy
n p^ (1-p^) >= 5
Here,
n p^ (1-p^) = 167*0.209580*(1-0.209580) = 27.6645
Hence, the requirement is satisfied.
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c)
Note that
p^ = point estimate of the population proportion = x / n = 35/167 = 0.20958083
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.031495339
Now, for the critical z,
alpha/2 = 0.005
Thus, z(alpha/2) = 2.575829304
Thus,
Margin of error = z(alpha/2)*sp = 0.081126616
lower bound = p^ - z(alpha/2) * sp = 0.128454222
upper bound = p^ + z(alpha/2) * sp = 0.290707454
Thus, the confidence interval is
( 0.128454222 , 0.290707454 ) [ANSWER]
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d)
We are 95% confident that the true proportion of those who received 10 mg of a drug daily and reported head ache as a side effect is between 0.12845 and 0.29071.
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