Confidence intervals worksheet with answers

Free printable Confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
n = 200, σ = 25L = ?Ux̄ = 44.5E99%

A sample of 200 measurements has mean 44.5. The population standard deviation is known to be 25. Find the lower limit of the 99% confidence interval for the mean.

n = 200x̄ = 44.5σ = 2599%
lower limit =
2.Easy
n = 121, σ = 19L = ?Ux̄ = 82.5E90%

A sample of 121 measurements has mean 82.5. The population standard deviation is known to be 19. Find the lower limit of the 90% confidence interval for the mean.

n = 121x̄ = 82.5σ = 1990%
lower limit =
3.Medium
μ₁ − μ₂0L = ?Ux̄₁ − x̄₂E99%

The battery life of two phone models is compared. Model 1: 60 phones, mean 80 h, known standard deviation 18 h. Model 2: 50 phones, mean 66.5 h, known standard deviation 18 h. Find the lower limit of the 99% confidence interval for μ₁ − μ₂.

n₁ = 60x̄₁ = 80 hσ₁ = 18 hn₂ = 50x̄₂ = 66.5 hσ₂ = 18 h99%
lower limit = h
4.Medium
x̄E₁ = 2.690%, n = 100x̄E₂ = ?90%, n = 200

A 90% confidence interval for a mean, based on 100 observations and a known σ, has a margin of error of 2.6. What is the margin of error E₂ if the same study uses 200 observations instead?

90%n₁ = 100E₁ = 2.6n₂ = 200
E₂ =
5.Hard
n = 20σ = ?Us = 3.395%

The diameters of 20 machined shafts have a sample standard deviation of 3.3 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 19, 2.5% of the χ² distribution lies below 8.907 and 2.5% lies above 32.852.

n = 20s = 3.3 µmχ² = 8.907, 32.852
σ = µm
6.Hard
μ₁ − μ₂, t(24) = 2.7970LU = ?x̄₁ − x̄₂E99%

Two fertilisers are tested. Plot group 1: 8 plots, mean yield 76 kg, standard deviation 6.5 kg. Plot group 2: 18 plots, mean 78 kg, standard deviation 8.5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the upper limit of the 99% confidence interval for μ₁ − μ₂.

n₁ = 8x̄₁ = 76s₁ = 6.5n₂ = 18x̄₂ = 78s₂ = 8.599%t(24) = 2.797
upper limit = kg

Answer key

  1. 1. lower limit = 39.95
  2. 2. lower limit = 79.66
  3. 3. lower limit = 4.621 h
  4. 4. E₂ = 1.838
  5. 5. σ = 2.51 µm
  6. 6. upper limit = 7.471 kg

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