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Sampling Distribution

\(\sigma_\bar{x}\) calculator \(\sigma_\bar{x}\) finite population \(\sigma_{\bar{x_1} - \bar{x_2}}\) calculator

\(\sigma_\bar{p}\) calculator \(\sigma_\bar{p}\) Finite Population \(\sigma_{\bar{p_1} - \bar{p_2}}\) calculator

Standard Error of Proportion

Is your population proportion known? Yes No

Sample Size

Population Size

Proportion

Sample Proportion

Result

Please enter all values.

Tips about Hypothesis testing for Mean when σ known:

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Definations

• The standard error of the proportion measures the variability of a sample proportion from the true population proportion. When dealing with a finite population, the calculation needs to account for the population size to be more accurate. This adjustment is known as the finite population correction factor.
• The formula for the standard error of the proportion with the finite population correction factor is: \[ \sigma_p = \sqrt{\frac{p(1 - p)}{n}} \times \sqrt{\frac{N - n}{N - 1}} \]
• For an unknown population proportion (using sample proportion: \[ \sigma_{\hat{p}} = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \times \sqrt{\frac{N - n}{N - 1}} \]
Where:
\(p\) is Population Proportion
\(\hat{p}\) is sample proportion \(n\) is a sample size \(N\) is a population size

Common Errors:

1. Ignoring Finite Population Correction:
   • When the sample size is a significant fraction of the population (n/N ≥ 5%), ignoring the correction factor can lead to overestimating the variability.
2. Misidentifying Proportions:
   • Ensure you correctly distinguish between sample proportion (\(\hat{p}\)) and population proportion (p).
3. Incorrect Formula Application:
   • Use the finite population correction only when the sample size is a significant fraction of the population. For small samples relative to the population, the correction factor has negligible impact.
4. Rounding Errors:
   • Use precise values during calculations to avoid rounding errors that can affect the final result.

Additional Tips

1. When to Use Correction Factor:
   • Apply the finite population correction factor if your sample size is more than 5% of the total population. For large populations where n/N < 5%, the correction factor is minimal and can be ignored.
2. Verify Population Size:
   • Ensure the total population size (N) is correctly identified, as this significantly impacts the correction factor.
3. Increasing the sample size
   • If the sample size increases and close to the popoulation size then the standard error become close to zero. and if it is the n equals with the N then the standard erro will be 0.