- 2070 Chaitra · 4 marks
CI: mean pH in rainfalls
Short answer
With n=40, use normal z-interval: x̄ ± 2.576·s/√n. SE=0.0791, margin=0.2036. 99% confidence interval for mean pH is (6.50, 6.90).
An analysis for pH (acidity) in a random sample of water from 40 rainfalls showed that mean is 6.7 and s.d. is 0.5. Find a 99% confidence interval for the mean pH in rainfalls.
The sample is large (n = 40), so the normal interval x̄ ± z·s/√n is used, with s as the estimate of σ.
n = 40, x̄ = 6.7, s = 0.5
SE = s/√n = 0.5/√40 = 0.0791
99% CI: z = 2.576
margin = 2.576 × 0.0791 = 0.2036
limits = 6.7 ± 0.2036 = (6.496, 6.904)
Answer: 99% confidence interval for mean pH = (6.50, 6.90).
✓ Answer checked by Claude Sonnet 5.5
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