🎓 Statistics & Data • Hypothesis Testing
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Z-Test Calculator
Calculates Z-test statistic and compares against critical values (±1.96 for α = 0.05).
Significance Level (α):
One-Sample Z-Test for Population Mean
Standard Z-Test: z = (x̄ - μ₀) / (σ / √n)
Test hypotheses about a population mean when the population standard deviation σ is known.
Standard Z-Score Test Statistic
z = 2.4
Reject Null Hypothesis H₀ (z = 2.4, p = 0.0164 < α = 0.05)
P-Value0.0164
Standard Error1
Critical Z±1.96
Alpha (α)0.05
What is a Z-Test?
A Z-test is a statistical hypothesis test used when the dataset follows a normal distribution and the population standard deviation σ is known.
Formula & Step-by-Step Calculation
z = (x̄ - μ₀) / (σ / √n)
Standardized deviation of the sample mean.
Worked Step-by-Step Examples
Example 1
Sample mean 52.4, target 50.0, σ = 8.0, n = 64
Solution: z = +2.40 (Reject H₀, p = 0.0164)
• SE = 8 / √64 = 1.0; z = (52.4 - 50.0) / 1.0 = 2.40
Common Real-World & Academic Use Cases
- ✓ Manufacturing assembly line weight calibration
- ✓ Financial returns benchmark comparison
- ✓ Demographic census parameter testing
How to Use the Z-Test Calculator
1
Enter Sample Data
Input sample mean x̄ and n.
2
Enter Population Parameters
Input μ₀ and σ.
3
View Z Statistic
Review statistical significance.
Frequently Asked Questions
Q: What is the critical Z value for a 95% confidence level?
±1.96 for a two-tailed test, or +1.645 for a one-tailed test.