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Standard Error Formula:
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The Standard Error (SE) of a proportion measures the variability or precision of a sample proportion as an estimate of the population proportion. It quantifies how much the sample proportion is expected to fluctuate from the true population proportion.
The calculator uses the Standard Error formula:
Where:
Explanation: The formula shows that as sample size increases, the standard error decreases, indicating more precise estimates of the population proportion.
Details: Calculating standard error is essential for constructing confidence intervals and conducting hypothesis tests about population proportions. It helps researchers determine the precision of their estimates and make inferences about the population.
Tips: Enter the population standard deviation and sample size. Both values must be positive numbers, with sample size being at least 1.
Q1: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability in the data, while standard error measures the precision of a sample statistic as an estimate of the population parameter.
Q2: When should I use this standard error formula?
A: Use this formula when you know the population standard deviation and want to estimate the precision of a sample proportion.
Q3: How does sample size affect standard error?
A: As sample size increases, standard error decreases, leading to more precise estimates of the population parameter.
Q4: Can standard error be zero?
A: Standard error approaches zero as sample size approaches infinity, but in practice, it's never exactly zero with finite samples.
Q5: What if I don't know the population standard deviation?
A: If population standard deviation is unknown, you would typically use the sample standard deviation and possibly a t-distribution instead.