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The problem asks for the sample proportion \(\hat{p}\), given a confidence interval for the proportion of accountants who double-check their work.

The confidence interval provided is \((0.89, 0.97)\).

To estimate the sample proportion \(\hat{p}\), we typically use the midpoint of the confidence interval. This can be calculated as follows:

\[
\hat{p} = \frac{\text{lower bound} + \text{upper bound}}{2} = \frac{0.89 + 0.97}{2} = \frac{1.86}{2} = 0.93
\]

So, the sample proportion \(\hat{p}\) is 0.93.

Would you like further clarification or details on how this is computed? 

Here are five related questions to explore:

1. How is a confidence interval constructed in statistics?
2. What does the sample proportion represent in a survey?
3. How do you interpret a confidence interval in terms of probability?
4. What is the margin of error in a confidence interval?
5. How would increasing the sample size affect the width of the confidence interval?

**Tip:** The midpoint of the confidence interval is a good estimate of the sample proportion when no other data is provided.

A random sample of accountants were asked whether they double-check their calculations on a tax form. The resulting confidence interval for the proportion of accountants who double-check their work is (0.89, 0.97). What is the sample proportion, p̂?

Learn how to calculate the sample proportion from a given confidence interval in statistics. This problem involves using the formula p̂ = (lower bound + upper bound) / 2 with a detailed example where the interval is (0.89, 0.97). Suitable for students in Grades 11-12 or introductory college level.

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