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Z Score Formula for Proportion:
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The Z Score for Proportion is a statistical measure that quantifies how many standard deviations a sample proportion is from the hypothesized population proportion. It's used in hypothesis testing for proportions.
The calculator uses the Z Score formula for proportion:
Where:
Explanation: The formula measures the standardized difference between the observed sample proportion and the expected population proportion under the null hypothesis.
Details: Z Score calculation is crucial for hypothesis testing of proportions, determining statistical significance, and making inferences about population parameters based on sample data.
Tips: Enter sample proportion (0 to 1), hypothesized proportion (0 to 1), and sample size (positive integer). All values must be valid within their specified ranges.
Q1: When should I use the Z Score for proportion test?
A: Use it when testing hypotheses about population proportions, typically when sample size is large enough (n > 30) and both np₀ and n(1-p₀) are greater than 5.
Q2: What does a high absolute Z Score value indicate?
A: A high absolute Z Score (typically > 1.96 or < -1.96 for 95% confidence) indicates that the sample proportion is significantly different from the hypothesized proportion.
Q3: Can this test be used for small sample sizes?
A: For small sample sizes (n < 30), the exact binomial test is more appropriate than the Z test for proportions.
Q4: What are the assumptions of this test?
A: The test assumes random sampling, independence of observations, and that the sample size is sufficiently large for the normal approximation to be valid.
Q5: How is this different from the t-test for proportions?
A: For large samples, the Z test is appropriate. For smaller samples, some statisticians prefer using a t-test with continuity correction, though the exact binomial test is often recommended.