c.c.

If you wanted to conduct a​ follow-up study to estimate the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization to within 

plus or minus 0.03±0.03 

with 

95 %95% 

​confidence, how many nonprofits would you​ survey?

A sample of 

enter your response here 

nonprofits should be surveyed. ​(Round up to the nearest​ integer.)  

To determine how many nonprofits should be surveyed, we can use the formula for sample size calculation in estimating a population proportion. The formula is:

\[
n = \frac{{Z^2 \cdot p \cdot (1 - p)}}{{E^2}}
\]

Where:
- \(n\) is the required sample size
- \(Z\) is the z-value corresponding to the desired confidence level
- \(p\) is the estimated population proportion (if no estimate is available, use \(p = 0.5\) for the most conservative sample size)
- \(E\) is the margin of error

### Given:
- Confidence level = 95% → \(Z = 1.96\)
- Margin of error \(E = 0.03\)
- \(p = 0.5\) (since we are not given an estimated proportion)

Now, plug the values into the formula:

\[
n = \frac{{(1.96)^2 \cdot 0.5 \cdot (1 - 0.5)}}{{(0.03)^2}}
\]

\[
n = \frac{{(3.8416) \cdot 0.5 \cdot 0.5}}{{0.0009}}
\]

\[
n = \frac{{0.9604}}{{0.0009}} = 1067.11
\]

Since the sample size must be a whole number, we round up to the nearest integer, which gives us:

\[
n = 1068
\]

So, **1068 nonprofits should be surveyed**.

---

Would you like further clarification or details on this calculation?

### Related Questions:
1. What factors affect the required sample size in a survey?
2. How does changing the confidence level affect the sample size?
3. How can you estimate the population proportion if no prior information is available?
4. What happens to the sample size if the margin of error is reduced?
5. How would the calculation change if we used a different confidence interval, like 90%?

**Tip:** When no prior estimate for the proportion is available, using \(p = 0.5\) ensures the maximum possible sample size, leading to a more conservative estimate.

If you wanted to conduct a follow-up study to estimate the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization to within plus or minus 0.03 with 95% confidence, how many nonprofits would you survey? A sample of nonprofits should be surveyed. (Round up to the nearest integer.)

Discover how to calculate the sample size required to survey nonprofits, ensuring a 95% confidence level and a margin of error of 0.03. Using the statistical sample size formula, this example walks through the calculation step-by-step, showing why 1068 nonprofits should be surveyed. Suitable for undergraduate students or professionals in survey analysis.

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