Question

use the sample data and confidence level given below to complete parts (a) through (d)
a drug is used to help prevent blood clots in certain patients. in clinical trials, among 4829 patients treated with
the drug, 115 developed the adverse reaction of nausea. construct a 90% confidence interval for the proportion of
adverse reactions
(round to three decimal places as needed)
b) identify the value of the margin of error e.
e = 0.004
(round to three decimal places as needed)
c) construct the confidence interval
0.020 < p < 0.028
(round to three decimal places as needed)
d) write a statement that correctly interprets the confidence interval. choose the correct answer below
a. one has 90% confidence that the sample proportion is equal to the population proportion
b. one has 90% confidence that the interval from the lower bound to the upper bound actually does contain
the true value of the population proportion.
c. there is a 90% chance that the true value of the population proportion will fall between the lower bound and
the upper bound
d. 90% of sample proportions will fall between the lower bound and the upper bound

Explanation:

A confidence interval gives a range of values within which the true population parameter (here, the proportion of patients having the adverse reaction) is likely to lie. The interpretation of a confidence interval is that we are \(x\%\) (in this case \(90\%\)) confident that the interval contains the true population parameter. Option A is incorrect because the sample proportion is just a point - estimate and not equal to the population proportion in most cases. Option C is wrong as it implies a probability about the population proportion being in the interval, but the population proportion is a fixed value. Option D is incorrect as it refers to sample proportions instead of the population proportion.

Answer:

B. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.