For the following questions, information about a sample is given. Assuming the sampling distribution is symmetric and bell-shaped, use the information to give a 95% confidence interval, and indicate the parameter being estimated.

p
^
= 0.35 and the standard error is 0.04. Give your answer to 4 decimal places. Find the confidence interval

To find a 95% confidence interval for a proportion, we can use the formula:

\[
CI = \hat{p} \pm Z \times SE
\]

Where:
- \(\hat{p} = 0.35\) (the sample proportion),
- \(SE = 0.04\) (the standard error),
- \(Z\) is the critical value for a 95% confidence level from the standard normal distribution (which is approximately 1.96).

Now, we'll calculate the margin of error:

\[
Margin \ of \ Error = Z \times SE = 1.96 \times 0.04 = 0.0784
\]

Then, we can compute the confidence interval by adding and subtracting this margin of error from \(\hat{p}\):

\[
CI = 0.35 \pm 0.0784
\]

Thus, the confidence interval is:

\[
CI = (0.35 - 0.0784, 0.35 + 0.0784) = (0.2716, 0.4284)
\]

### Final Answer:
The 95% confidence interval is **(0.2716, 0.4284)**, and the parameter being estimated is the population proportion, \(p\).

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Do you have any questions or would you like further details? Here are 5 related questions to explore further:

1. How is the critical value for a confidence level determined?
2. What is the significance of the standard error in constructing confidence intervals?
3. Can we apply this method if the sampling distribution is not symmetric and bell-shaped?
4. How would a 99% confidence interval change the result?
5. What assumptions underlie the construction of a confidence interval for proportions?

**Tip:** The margin of error decreases with larger sample sizes, which tightens the confidence interval.

For the following questions, information about a sample is given. Assuming the sampling distribution is symmetric and bell-shaped, use the information to give a 95% confidence interval, and indicate the parameter being estimated.
p^ = 0.35 and the standard error is 0.04. Give your answer to 4 decimal places. Find the confidence interval.

Learn how to calculate a 95% confidence interval for a proportion, where the sample proportion is 0.35 and the standard error is 0.04. This problem demonstrates the use of key statistical concepts, such as confidence intervals, the normal distribution, and the Central Limit Theorem. Suitable for students in Grades 10-12.

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