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
164.18x̄172.8290%

A 90% confidence interval for a mean, computed from 64 observations with a known population standard deviation, is [164.18, 172.82]. What standard deviation σ was used?

[164.18, 172.82]n = 6490%
σ =
2.Easy
n = 200, σ = 24L = ?Ux̄ = 21.5E90%

A sample of 200 measurements has mean 21.5. The population standard deviation is known to be 24. Find the lower limit of the 90% confidence interval for the mean.

n = 200x̄ = 21.5σ = 2490%
lower limit =
3.Medium
n = 7, s = 5.5LU = ?x̄ = 47E90%

A sample of 7 items has mean 47 and standard deviation s = 5.5. The population is roughly normal. Find the upper limit of the 90% confidence interval for the mean.

n = 7x̄ = 47s = 5.590%t(6) = 1.943
upper limit =
4.Medium
n = 13, s = 7LUx̄ = 69.5E = ?90%

A sample of 13 items has mean 69.5 and standard deviation s = 7. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 13x̄ = 69.5s = 790%t(12) = 1.782
E =
5.Hard
μ₁ − μ₂, t(24) = 1.7110L = ?Ux̄₁ − x̄₂E90%

Two fertilisers are tested. Plot group 1: 11 plots, mean yield 60 kg, standard deviation 7.5 kg. Plot group 2: 15 plots, mean 61.5 kg, standard deviation 6.5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the lower limit of the 90% confidence interval for μ₁ − μ₂.

n₁ = 11x̄₁ = 60s₁ = 7.5n₂ = 15x̄₂ = 61.5s₂ = 6.590%t(24) = 1.711
lower limit = kg
6.Hard
σ = 36, n = ?x̄ − Ex̄ + Ex̄E = 1.595%

The population standard deviation is 36. 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 1.5?

σ = 36E = 1.595%
n =

Answer key

  1. 1. σ = 21.01
  2. 2. lower limit = 18.71
  3. 3. upper limit = 51.04
  4. 4. E = 3.46
  5. 5. lower limit = −6.21 kg
  6. 6. n = 2213

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