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Sample Error of Proportion Formula:
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The sample error of proportion (also known as standard error of proportion) measures the variability or uncertainty in a sample proportion estimate. It quantifies how much the sample proportion is expected to vary from the true population proportion.
The calculator uses the sample error formula:
Where:
Explanation: The formula calculates the standard deviation of the sampling distribution of the proportion, indicating how much the sample proportion would vary across different samples from the same population.
Details: Calculating the sample error of proportion is essential for constructing confidence intervals, conducting hypothesis tests, and determining the precision of proportion estimates in statistical analysis and research studies.
Tips: Enter the sample proportion as a decimal between 0 and 1, and the sample size as a positive integer. Both values are required for the calculation.
Q1: What is the range of valid values for proportion?
A: The proportion (p) must be between 0 and 1 inclusive, representing 0% to 100% respectively.
Q2: How does sample size affect the sample error?
A: As sample size increases, the sample error decreases. Larger samples provide more precise estimates of the population proportion.
Q3: When is this calculation most useful?
A: This calculation is particularly useful in survey research, quality control, medical studies, and any situation where you need to estimate a proportion from sample data.
Q4: What are the assumptions behind this formula?
A: The formula assumes random sampling, independence of observations, and that the sample size is sufficiently large (typically n ≥ 30).
Q5: How is sample error related to confidence intervals?
A: The sample error is used to construct confidence intervals for the population proportion. A 95% confidence interval is typically calculated as p ± 1.96 × SE.