Questions: 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 4460 patients treated with the drug, 139 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. 0.031 (Round to three decimal places as needed.) b) Identify the value of the margin of error E . E= (Round to three decimal places as needed.)

Solution Steps

The best point estimate of the population proportion \( p \) is calculated as follows:

\[ \hat{p} = \frac{x}{n} = \frac{139}{4460} \approx 0.031 \]

The standard deviation of the sample proportion is given by:

\[ \sigma = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = \sqrt{\frac{0.031(1 - 0.031)}{4460}} \approx 0.0026 \]

The margin of error \( E \) is calculated using the formula:

\[ E = Z \cdot \sigma = 1.96 \cdot 0.002601939805773202 \approx 0.000 \]

The 95% confidence interval for the proportion of adverse reactions is calculated as:

\[ \hat{p} \pm E = 0.031 \pm 1.96 \cdot \sqrt{\frac{0.031(1 - 0.031)}{4460}} \implies (0.026, 0.036) \]

Final Answer