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1 Sample Proportion Test Formula:
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The 1 Sample Proportion Test is a statistical hypothesis test used to determine whether a sample proportion differs significantly from a hypothesized population proportion. It calculates a z-score to assess the statistical significance of the observed difference.
The calculator uses the 1 sample proportion test formula:
Where:
Explanation: The formula calculates how many standard errors the sample proportion is away from the hypothesized proportion, providing a measure of statistical significance.
Details: The z-score helps determine whether the observed sample proportion is statistically significantly different from the hypothesized proportion, which is crucial for hypothesis testing in various research and quality control applications.
Tips: Enter the sample proportion (between 0 and 1), hypothesized proportion (between 0 and 1), and sample size (positive integer). All values must be valid for accurate calculation.
Q1: What does the z-score represent?
A: The z-score represents how many standard errors the sample proportion is away from the hypothesized proportion. Larger absolute values indicate stronger evidence against the null hypothesis.
Q2: When is this test appropriate?
A: This test is appropriate when you have a large sample size (n > 30) and want to test if a sample proportion differs from a known or hypothesized population proportion.
Q3: How do I interpret the z-score?
A: Typically, |z| > 1.96 suggests statistical significance at the 0.05 level, and |z| > 2.58 suggests significance at the 0.01 level (for a two-tailed test).
Q4: What are the assumptions of this test?
A: The test assumes random sampling, independence of observations, and that np₀ and n(1-p₀) are both greater than 5 to ensure normal approximation.
Q5: Can this test be used for small samples?
A: For small samples, the exact binomial test is more appropriate as the normal approximation may not hold well.