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0.05═══ Verdict ═══
✗ Fail to reject H₀: p = 0.642415 ≥ α = 0.05
ℹ H₀: μ = 25.0000 H₁: μ ≠ 25.0000 (two-tailed)
ℹ One-sample t-test, df 9: statistic -0.4804, critical ±2.2622
ℹ Effect size: Cohen's d = -0.152 (negligible)
⚠ Normality: not testable with n = 10; judge from the histogram and be cautious
═══ Hypotheses and Decision Rule ═══
Null hypothesis (H₀): μ = 25.0000
Alternative (H₁): μ ≠ 25.0000
Significance level (α): 0.05
Tail: two-tailed
Test statistic: t = (x̄ − μ₀) / (s/√n)
Critical value: 2.2622
Rejection region: t ≤ -2.2622 or t ≥ 2.2622
Observed statistic: -0.4804 → outside the rejection region
Fix α and the direction before seeing the data; changing either afterwards is not a valid test.
═══ Sample ═══
n: 10
Sample mean: 24.8000
Sample std dev (n-1): 1.3166
Standard error: 0.4163
Degrees of freedom: 9
p-value: 0.642415
95% CI for μ: 23.8582 to 25.7418
The CI contains μ₀ = 25.0000, which matches the decision above.
═══ Effect Size and Power ═══
Difference from μ₀: -0.2000
Cohen's d: -0.1519 (negligible)
Approximate power at the observed effect: 3.7%
n needed for 80% power at this effect: 342
⚠ Post-hoc power computed from the observed effect is a known trap: it is just a restatement of the p-value. Use it to plan the next study, not to judge this one.
═══ Assumptions ═══
Skewness (G1): 0.0876
Excess kurtosis (G2): -0.7513
D'Agostino-Pearson K²: needs n ≥ 20 (n = 10)
Jarque-Bera: 0.4015 (p 0.818125)
✓ No outliers beyond the 1.5×IQR fences
⚠ n = 10: the t-test needs roughly normal data at this size
Observations must be independent and drawn from one population.
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Test statistical hypotheses with detailed results. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.