Let's solve both parts of the question systematically.

(a) Point Estimate of the Proportion

The point estimate is the sample proportion, $\hat{p}$, which is calculated by dividing the number of patients with high blood pressure by the total number of patients in the sample.

$\hat{p} = \frac{\text{Number of patients with high blood pressure}}{\text{Total number of patients}} = \frac{103}{355}$

$\hat{p} \approx 0.2901$

So, the point estimate of the proportion of patients with high blood pressure is 0.2901 (rounded to 4 decimal places).

(b) Margin of Error

The margin of error (ME) is the difference between the upper bound of the confidence interval and the point estimate, or equivalently, the difference between the point estimate and the lower bound.

$\text{Margin of Error} = \text{Upper Bound} - \hat{p} = 0.3462 - 0.2901 = 0.0561$

Thus, the margin of error is 0.0561 (rounded to 4 decimal places).

Final Answers:

• Point estimate = 0.2901
• Margin of error = 0.0561

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Do you want more details on how to compute confidence intervals or any other clarifications?

Here are 5 related questions to expand your understanding:

1. How would you calculate the sample standard deviation in this context?
2. What does a 98% confidence interval mean in terms of interpretation?
3. How would the confidence interval change if the confidence level were reduced to 90%?
4. What formula is used to construct a confidence interval for a proportion?
5. How can we check if a larger sample size is needed for a more precise estimate?

Tip: Increasing the sample size decreases the margin of error, leading to more precise estimates of population parameters.