In a random sample of 355  patients of a primary care doctor, it was found that 103 have high blood pressure and 252  do not. A 98% confidence interval was constructed to estimate the proportion of all patients that have high blood pressure. This confidence interval came out to be (.2341, .3462). What is a point estimate of the proportion of all patients that have high blood pressure?

Answer =  Round to 4 decimal places.

(b) What is the margin of error?

Answer =  Round to 4 decimal places.

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.

In a random sample of 355 patients of a primary care doctor, it was found that 103 have high blood pressure and 252 do not. A 98% confidence interval was constructed to estimate the proportion of all patients that have high blood pressure. This confidence interval came out to be (.2341, .3462). What is a point estimate of the proportion of all patients that have high blood pressure? (b) What is the margin of error?

Learn how to calculate the point estimate and margin of error for a proportion using a sample of 355 patients. This example explores the construction of a 98% confidence interval for patients with high blood pressure and covers key statistical concepts such as proportion, confidence intervals, and margin of error.

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