Explore the sampling distribution of the sample proportion with our advanced online calculator. Instantly compute the mean and standard error (standard deviation) for any given population proportion and sample size. Perfect for students, researchers, and professionals needing quick, accurate statistical calculations. Easily determine Z-scores for specific sample proportions. Improve your understanding of inferential statistics and hypothesis testing today.
Formula:
Formulas Used:
Mean of the Sample Proportion (μp̂):
μp̂ = p
Standard Error of the Sample Proportion (σp̂):
σp̂ = √((p(1-p))/n)
Z-score for a Sample Proportion (Z):
Z = (p̂ - μp̂) / σp̂
Where:
- p = Population proportion (the true proportion of success in the population)
- n = Sample size
- p̂ = Sample proportion (the proportion of success observed in the sample)
- μp̂ = Mean of the sampling distribution of the sample proportion
- σp̂ = Standard error of the sampling distribution of the sample proportion