To solve part (a) of the question, we are tasked with finding the best point estimate of the population proportion $p$, given the following information:

• Total number of patients treated: $n = 4608$
• Number of patients who developed adverse reactions: $x = 167$

Formula for Point Estimate

The best point estimate for the population proportion is given by: $\hat{p} = \frac{x}{n}$

Substitute the given values: $\hat{p} = \frac{167}{4608}$

Calculation

$\hat{p} = 0.0362$

Final Answer

The best point estimate of the population proportion $p$ is: $\boxed{0.036}$ (rounded to three decimal places as requested).

Would you like me to proceed with constructing the confidence interval (part b), or provide more detailed explanations for any of these steps?

Here are 5 related questions to expand your understanding:

1. What is the formula for constructing a confidence interval for a population proportion?
2. How does the choice of confidence level (e.g., 99%) affect the width of the confidence interval?
3. What conditions must be satisfied to use the normal approximation for constructing the confidence interval?
4. How do you calculate the margin of error for a population proportion?
5. What does the best point estimate tell us about the population?

Tip: Always verify that the sample size is large enough to use the normal approximation by checking $n \hat{p} \geq 5$ and $n(1 - \hat{p}) \geq 5$.