🎓 Statistics & Data • Hypothesis Testing
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Student’s T-Test Calculator (One-Sample & Two-Sample)
Calculates t-statistic, degrees of freedom, and hypothesis rejection decisions when population variance is unknown.
Significance Level (α):
One-Sample Student's T-Test
Student's T-Test: t = (x̄ - μ₀) / (s / √n)
Test whether a sample mean significantly differs from a hypothesized population mean when population variance is unknown.
Presets:
Student's T-Statistic Result
t = 2.0833
Reject Null Hypothesis H₀ (p = 0.0382 < α = 0.05)
P-Value0.0382
Deg of Freedom (df)24
Standard Error (SE)2.4
Alpha Threshold (α)0.05
Sampling Distribution Curve with Critical Rejection Regions (α = 0.05)
Rejection Region (|t| ≥ t_crit) Calculated t = 2.0833
What is Student’s T-Test?
Student’s t-test compares sample means to determine if they are statistically different from a hypothesized population mean or each other.
Formula & Step-by-Step Calculation
t = (x̄ - μ₀) / (s / √n), df = n - 1
Difference between sample and hypothesized mean scaled by standard error.
Worked Step-by-Step Examples
Example 1
Sample mean 105, hypothesized mean 100, s = 12, n = 25
Solution: t = 2.083 (df = 24, p < 0.05 ⟹ Reject H₀)
• SE = 12 / √25 = 2.4; t = (105 - 100) / 2.4 = 2.0833
Common Real-World & Academic Use Cases
- ✓ Testing drug efficacy vs placebo control group
- ✓ Comparing test scores between teaching methods
- ✓ Engineering material tensile strength validation
How to Use the Student’s T-Test Calculator (One-Sample & Two-Sample)
1
Input Sample Mean & Size
Enter x̄ and n.
2
Input Hypothesized Mean
Enter μ₀.
3
Read t-Score
Inspect degrees of freedom and statistical decision.
Frequently Asked Questions
Q: When do you use a t-test instead of a z-test?
Use a t-test when the population standard deviation σ is unknown and sample size n is small (< 30).