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Test: mean weight of ten objects is 65 g

Short answer

One-sample t-test: n = 9, mean = 65.07 g, t = 0.108, df = 8. At α = 0.05, critical value = ±2.306; fail to reject H0. The data support the suggestion that the population mean weight is 65 g.

Ten objects were chosen at random from the large population and their weights were found to be in grams 63, 63, 64, 65, 66, 69, 65, 66.1, 64.5. In the light of above data, discuss the suggestion that the mean weight in the population is 65 gm. Use α = 0.05.

Population SD is unknown and the sample is small, so a one-sample t-test is used. (Only nine weights are listed although the question says ten objects; the nine given values are used, n = 9.)

  1. H0: μ = 65 g H1: μ ≠ 65 g (two-tailed)
  2. Level of significance: α = 0.05
  3. Sample values and test statistic:
n = 9, Σx = 585.6, x̄ = 65.0667
s² = Σ(x−x̄)²/(n−1) = 27.4200/8 = 3.4275,  s = 1.8514
t = (x̄ − μ₀)/(s/√n) = (65.0667 − 65)/(1.8514/√9) = 0.0667/0.6171 = 0.108
  1. Critical value: t at α = 0.05, df = n−1 = 8: ±2.306. Reject H0 if |t| > 2.306.
  2. Decision: the calculated value falls in the acceptance region (p-value = 0.9166), so fail to reject H0.

Conclusion: the data are consistent with the suggestion that the population mean weight is 65 g.

✓ Answer checked by Claude Sonnet 5.5

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