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Test: electrification effect on barley tillers

Short answer

Pooled two-sample t-test: t = (23.333−17.625)/1.869 = 3.055, df=15, critical t=±2.131. Reject H0; electrification significantly affects tillering. Caged pots had higher mean tillers (23.33 vs 17.62).

Eight pots growing barley plants each were exposed to a high tension discharge, while nine similar pots were enclosed in an earthed wire cage. The number of tillers in each pot were as follows:

Caged172718252729272317
Electrified1616201620171521
Test the hypothesis whether electrification exercises have any real effect on the tillering at α = 0.05 level of significance.

The samples are small and independent, with unknown variances assumed equal, so a pooled two-sample t-test is used.

  1. H0: μ₁ = μ₂ (electrification has no effect on tillering) H1: μ₁ ≠ μ₂ (two-tailed)
  2. Level of significance: α = 0.05
  3. Sample statistics:
Caged:       n₁ = 9, Σx = 210, Σx² = 5084
             x̄₁ = 210/9 = 23.333,  s₁² = 23.000
Electrified: n₂ = 8, Σx = 141, Σx² = 2523
             x̄₂ = 141/8 = 17.625,  s₂² = 5.411

Sp² = [(n₁−1)s₁² + (n₂−1)s₂²]/(n₁+n₂−2)
    = [8×23.000 + 7×5.411]/15 = 14.792,  Sp = 3.846
SE  = Sp·√(1/n₁ + 1/n₂) = 3.846 × √(1/9 + 1/8) = 1.869
t   = (x̄₁ − x̄₂)/SE = (23.333 − 17.625)/1.869 = 3.055
  1. Degrees of freedom = n₁ + n₂ − 2 = 15. Critical value: t(0.025; 15) = ±2.131. Reject H0 if |t| > 2.131.
  2. Decision: |t| = 3.055 > 2.131 (p-value = 0.008), so reject H0.

Conclusion: electrification has a real (significant) effect on tillering at the 5% level; the caged pots produced more tillers on average (23.33 against 17.62).

✓ Answer checked by Claude Sonnet 5.5

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