Find the standard error. Round the answers to at least four decimal places, if necessary.

### Finding the Standard Error

The standard error (SE) of the sample proportion can be calculated using the formula:

\[
SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
\]

where:
- \(\hat{p}\) is the sample proportion,
- \(n\) is the sample size.

From the previous step, we know that \(\hat{p} = 0.5000\) and \(n = 96\).

Now we can plug these values into the formula to calculate the standard error:

\[
SE = \sqrt{\frac{0.5000 \times (1 - 0.5000)}{96}}
\]

Let's calculate it step by step:

1. Calculate \(\hat{p} \times (1 - \hat{p})\):

\[
0.5000 \times (1 - 0.5000) = 0.5000 \times 0.5000 = 0.2500
\]

2. Divide by \(n\):

\[
\frac{0.2500}{96} = 0.0026041667
\]

3. Take the square root:

\[
SE = \sqrt{0.0026041667} \approx 0.0510
\]

So, the standard error is:

\[
SE = 0.0510
\]

Would you like further details or have any questions?

Here are five questions you might find interesting:
1. Why is the standard error important in statistical analysis?
2. How does increasing the sample size affect the standard error?
3. What is the difference between standard deviation and standard error?
4. Can the standard error be zero? Why or why not?
5. How is the standard error used in constructing confidence intervals?

**Tip:** Remember, the standard error decreases as the sample size increases, providing a more precise estimate of the population parameter.

Learn how to find the standard error (SE) in statistics using the sample proportion and sample size. This guide provides a detailed calculation example and explains the importance of standard error in statistical analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation