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.


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

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

Where:
- \(\hat{p} = 0.40\) (the sample proportion)
- Margin of error \(= 0.034\)

Thus, the confidence interval is:

\[
(0.40 - 0.034, 0.40 + 0.034) = (0.366, 0.434)
\]

So, the confidence interval is:

\[
(0.366, 0.434)
\]

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.

A sample of voters were polled to determine the likelihood 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.

Learn how to calculate the confidence interval for a poll determining voter support for measure 324. This example demonstrates statistical concepts like proportions and margin of error, using a sample proportion of 40% with a 3.4% margin of error. Suitable for students in Grades 10-12.

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