If we want to find the required sample size n for the interval estimation of the population proportion p, and no reasonable estimate of this proportion is available, we can use  p^=0.5
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When no reasonable estimate of the population proportion \( p \) is available, we often use \( \hat{p} = 0.5 \) to calculate the required sample size \( n \). This is because \( \hat{p} = 0.5 \) maximizes the sample size, ensuring the sample is large enough to achieve the desired confidence level and margin of error.

Would you like more details or have any questions?

1. Why does \( \hat{p} = 0.5 \) maximize the required sample size?
2. How is the formula for sample size derived for interval estimation of a population proportion?
3. What is the relationship between margin of error and sample size in proportion estimation?
4. How do confidence levels affect sample size in interval estimation?
5. What happens if a preliminary estimate for \( p \) is available?

**Tip:** Using \( \hat{p} = 0.5 \) provides a conservative estimate when the actual proportion is unknown, helping to avoid underestimating the required sample size.

If we want to find the required sample size n for the interval estimation of the population proportion p, and no reasonable estimate of this proportion is available, we can use p^=0.5.

Understand how to calculate the required sample size for interval estimation of a population proportion when no reasonable estimate is available, using p^ = 0.5. Learn about key statistical concepts such as interval estimation, confidence intervals, and how p^ = 0.5 provides a conservative sample size estimate for accurate results.

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