1.Easy
A 90% confidence interval for a mean, computed from 25 observations with a known population standard deviation, is [38.89, 48.11]. What standard deviation σ was used?
[38.89, 48.11]n = 2590%
σ =
Confidence intervals worksheet with answers
2.Easy
A sample of 64 measurements has mean 93.5. The population standard deviation is known to be 16. Find the margin of error E of a 95% confidence interval for the mean.
n = 64x̄ = 93.5σ = 1695%
E =
3.Medium
The battery life of two phone models is compared. Model 1: 80 phones, mean 58.5 h, known standard deviation 9 h. Model 2: 30 phones, mean 48 h, known standard deviation 18 h. Find the lower limit of the 99% confidence interval for μ₁ − μ₂.
n₁ = 80x̄₁ = 58.5 hσ₁ = 9 hn₂ = 30x̄₂ = 48 hσ₂ = 18 h99%
lower limit = h
4.Medium
The battery life of two phone models is compared. Model 1: 60 phones, mean 49.5 h, known standard deviation 5 h. Model 2: 30 phones, mean 62 h, known standard deviation 17 h. Find the lower limit of the 90% confidence interval for μ₁ − μ₂.
n₁ = 60x̄₁ = 49.5 hσ₁ = 5 hn₂ = 30x̄₂ = 62 hσ₂ = 17 h90%
lower limit = h
5.Hard
The diameters of 10 machined shafts have a sample standard deviation of 1.4 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 9, 2.5% of the χ² distribution lies below 2.7 and 2.5% lies above 19.023.
n = 10s = 1.4 µmχ² = 2.7, 19.023
σ = µm
6.Hard
The population standard deviation is 10. How large a sample n do you need so that a 90% confidence interval for the mean has a margin of error of at most 0.5?
σ = 10E = 0.590%
n =
Answer key
- 1. σ = 14.01
- 2. E = 3.92
- 3. lower limit = 1.646 h
- 4. lower limit = −17.71 h
- 5. σ = 0.963 µm
- 6. n = 1083
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