Math Problem Statement

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?

Solution

The problem asks for the sample proportion p^\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)(0.89, 0.97).

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

p^=lower bound+upper bound2=0.89+0.972=1.862=0.93\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 p^\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.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Sample Proportion

Formulas

Sample Proportion Calculation: p̂ = (lower bound + upper bound) / 2

Theorems

Properties of Confidence Intervals

Suitable Grade Level

Grades 11-12 or Introductory College Level