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
105.09x̄112.9190%

A 90% confidence interval for a mean, computed from 64 observations with a known population standard deviation, is [105.09, 112.91]. What standard deviation σ was used?

[105.09, 112.91]n = 6490%
σ =
2.Easy
n = 121, σ = 27L = ?Ux̄ = 198E99%

A sample of 121 measurements has mean 198. The population standard deviation is known to be 27. Find the lower limit of the 99% confidence interval for the mean.

n = 121x̄ = 198σ = 2799%
lower limit =
3.Medium
n = 21, s = 6LUx̄ = 41.5E = ?95%

A sample of 21 items has mean 41.5 and standard deviation s = 6. The population is roughly normal. Find the margin of error E of a 95% confidence interval for the mean.

n = 21x̄ = 41.5s = 695%t(20) = 2.086
E =
4.Medium
x̄E₁ = 7.890%, n = 64x̄E₂ = ?99%, n = 64

A 90% confidence interval for a mean, based on 64 observations and a known σ, has a margin of error of 7.8. What is the margin of error E₂ of a 99% interval from the same data?

90%n₁ = 64E₁ = 7.899%
E₂ =
5.Hard
σ = 30, n = ?x̄ − Ex̄ + Ex̄E = 2.595%

The population standard deviation is 30. How large a sample n do you need so that a 95% confidence interval for the mean has a margin of error of at most 2.5?

σ = 30E = 2.595%
n =
6.Hard
μ₁ − μ₂, t(10) = 1.8120LUx̄₁ − x̄₂E = ?90%

Two fertilisers are tested. Plot group 1: 6 plots, mean yield 97 kg, standard deviation 8 kg. Plot group 2: 6 plots, mean 89 kg, standard deviation 3 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the margin of error E of the 90% confidence interval for μ₁ − μ₂.

n₁ = 6x̄₁ = 97s₁ = 8n₂ = 6x̄₂ = 89s₂ = 390%t(10) = 1.812
E = kg

Answer key

  1. 1. σ = 19.02
  2. 2. lower limit = 191.7
  3. 3. E = 2.731
  4. 4. E₂ = 12.21
  5. 5. n = 554
  6. 6. E = 6.32 kg

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