Skip to main content

Test: mean voltage of two companies

Short answer

Using a pooled two-sample t-test (equal variances), Sp = 0.3464, t = 3.020, df = 21. At α = 0.05, critical value = ±2.080; |t| > 2.080, reject H0. The mean voltages of the two companies differ significantly.

There was a research on voltage supply by Batteries supplied by two companies. Both company claims same. But researcher suspects that there is significant difference between mean voltages between two companies. To test this, she selected independent samples from both company and in lab test the result were as follows:

nMeanSample Standard deviation
Company A133.59V0.3V
Company B103.15V0.4V
Test the researcher suspect was correct at 5% level of significance.

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

  1. H0: μ_A = μ_B (no difference in mean voltage) H1: μ_A ≠ μ_B (two-tailed)
  2. Level of significance: α = 0.05
  3. Test statistic (small samples, equal variances assumed, pooled t-test):
Sp² = [(n₁−1)s₁² + (n₂−1)s₂²] / (n₁+n₂−2)
    = [12×0.0900 + 9×0.1600] / 21 = 0.1200
Sp  = 0.3464
t   = (x̄₁ − x̄₂) / [Sp √(1/n₁ + 1/n₂)]
    = (3.59 − 3.15) / [0.3464 × √(1/13 + 1/10)]
    = 0.4400 / 0.1457 = 3.020
  1. Critical value: t at α = 0.05, df = n₁+n₂−2 = 21: ±2.080. Reject H0 if |t| > 2.080.
  2. Decision: the calculated value falls in the rejection region (p-value = 0.0065), so reject H0.

Conclusion: the researcher's suspicion is correct; the mean voltages of the two companies differ significantly.

✓ Answer checked by Claude Sonnet 5.5

Related questions

All Probability and Statistics chapter 6 questions →