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 4379 patients treated with the drug, 193 developed the adverse reaction of nausea. construct a 95% confidence interval for the proportion of adverse reactions.
a) find the best point estimate of the population proportion p.
0.044
(round to three decimal places as needed.)
b) identify the value of the margin of error e.
e = 0.006
(round to three decimal places as needed.)
c) construct the confidence interval.
□<p<□
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval for a proportion is given by $\hat{p}-E < p <\hat{p} + E$, where $\hat{p}$ is the point - estimate and $E$ is the margin of error.

Step2: Substitute the values

We know that $\hat{p}=0.044$ and $E = 0.006$.
Substitute into the formula:
For the lower bound: $0.044-0.006$
For the upper bound: $0.044 + 0.006$

Step3: Calculate the bounds

Lower bound: $0.044-0.006=0.038$
Upper bound: $0.044 + 0.006=0.050$

Answer:

$0.038 < p < 0.050$