Math Problem Statement

A sample of voters were polled to determine the likelyhood of measure 324 passing. The poll determined that 40 % of voters were in favor of the measure with a margin of error of 3.4 %. Find the confidence interval. Use ( ) in your notation.

Solution

To find the confidence interval for the proportion of voters in favor of measure 324, we use the formula:

Confidence Interval=(p^Margin of Error,p^+Margin of Error)\text{Confidence Interval} = (\hat{p} - \text{Margin of Error}, \hat{p} + \text{Margin of Error})

Where:

  • p^=0.40\hat{p} = 0.40 (the sample proportion)
  • Margin of error =0.034= 0.034

Thus, the confidence interval is:

(0.400.034,0.40+0.034)=(0.366,0.434)(0.40 - 0.034, 0.40 + 0.034) = (0.366, 0.434)

So, the confidence interval is:

(0.366,0.434)(0.366, 0.434)

Would you like further details on this, or any clarification?

Here are some related questions:

  1. What does the margin of error mean in this context?
  2. How is the confidence level related to the margin of error?
  3. How can the sample size affect the width of the confidence interval?
  4. What assumptions are made when calculating this confidence interval?
  5. How can we reduce the margin of error in future polls?

Tip: Increasing the sample size can reduce the margin of error, leading to a more precise confidence interval.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Interval
Margin of Error
Proportions

Formulas

Confidence Interval = (p̂ - Margin of Error, p̂ + Margin of Error)

Theorems

Central Limit Theorem
Normal Approximation for Proportions

Suitable Grade Level

Grades 10-12