In a trial of 275 patients who received 10-mg doses of a drug daily, 33 reported
ID: 3127735 • Letter: I
Question
In a trial of 275 patients who received 10-mg doses of a drug daily, 33 reported headache as a side effect. Use the information to complete (a) through (d) below. Obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache asa a side effect. p(hat)= (B) Verify that the requirments for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence satisfied? (C) Construct a 99% confidence interval for the population proportion of patients who receive the drug and report headaches as a side effect. The 99% confidence interval is (_,_) (D) Interpret the confidence interval. Which statement below best interprets the interval -We are 99% confident that the interval does not contain the true value of p. -There is 99% chance that the true value of p will not fail in the interval. -We are 99% confident that the interval contains the true value of p.
Explanation / Answer
a)
Note that
p^ = point estimate of the population proportion = x / n = 33/275 = 0.12 [ANSWER]
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b)
As this is a random sample, and
n p^ (1-p^) = 29.04 < 5,
then the requirement is satisfied.
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c)
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.019595918
Now, for the critical z,
alpha/2 = 0.005
Thus, z(alpha/2) = 2.575829304
Thus,
Margin of error = z(alpha/2)*sp = 0.05047574
lower bound = p^ - z(alpha/2) * sp = 0.06952426
upper bound = p^ + z(alpha/2) * sp = 0.17047574
Thus, the confidence interval is
( 0.06952426 , 0.17047574 ) [ANSWER]
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d)
We are 99% confident that the interval contains the true value of p. [ANSWER, C]
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