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Standard Error Formula:
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The standard error of proportion measures the variability or precision of a sample proportion estimate. It quantifies how much the sample proportion is expected to vary from the true population proportion.
The calculator uses the standard 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.
Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests for proportions. It helps determine the precision of the sample estimate and the reliability of statistical inferences.
Tips: Enter the sample proportion (value between 0 and 1) and sample size (positive integer). The calculator will compute the standard error of the proportion.
Q1: What is 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 (like proportion) as an estimate of the population parameter.
Q2: When is this formula appropriate to use?
A: This formula is appropriate when the sample size is sufficiently large (typically n > 30) and the sampling distribution can be approximated by a normal distribution.
Q3: How does sample size affect standard error?
A: As sample size increases, standard error decreases. Larger samples provide more precise estimates of the population proportion.
Q4: What are the assumptions for this calculation?
A: The main assumptions are that the sample is random and independent, and that the sample size is large enough for the normal approximation to be valid.
Q5: How is standard error used in confidence intervals?
A: Standard error is multiplied by the appropriate z-score to create the margin of error for confidence intervals: CI = p ± z × SE.