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 

44054405 

patients treated with the​ drug, 

185185 

developed the adverse reaction of nausea. Construct a 

9595​% 

confidence interval for the proportion of adverse reactions.

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Part 1

​a) Find the best point estimate of the population proportion p.

enter your response here

​(Round to three decimal places as​ needed.)

To find the best point estimate of the population proportion \( p \), we use the formula:

\[
\hat{p} = \frac{x}{n}
\]

where:
- \( x \) is the number of patients who developed the adverse reaction (nausea),
- \( n \) is the total number of patients treated.

From the problem:
- \( x = 185 \),
- \( n = 4405 \).

Now calculate \( \hat{p} \):

\[
\hat{p} = \frac{185}{4405} \approx 0.042
\]

Thus, the best point estimate of the population proportion \( p \) is:

\[
\hat{p} = 0.042
\]

Would you like further details or explanations on this?

Here are 5 follow-up questions:
1. How would you calculate the margin of error for a confidence interval?
2. What formula is used to construct a confidence interval for a population proportion?
3. How does increasing the confidence level affect the width of the confidence interval?
4. Why is the point estimate of a population proportion important in statistics?
5. What assumptions must be met for the confidence interval calculation to be valid?

**Tip:** Always check if the sample size is large enough to assume a normal distribution for proportions when constructing confidence intervals.

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 4405 patients treated with the drug, 185 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions.

This problem involves calculating a 95% confidence interval for the proportion of patients who developed adverse reactions in a clinical trial. With 4405 patients treated and 185 developing nausea, you'll learn to find the point estimate and confidence interval using statistical formulas.

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