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 = 80, σ = 5LUx̄ = 89.5E = ?95%

A sample of 80 measurements has mean 89.5. The population standard deviation is known to be 5. Find the margin of error E of a 95% confidence interval for the mean.

n = 80x̄ = 89.5σ = 595%
E =
2.Easy
n = 49, σ = 13L = ?Ux̄ = 108E90%

A sample of 49 measurements has mean 108. The population standard deviation is known to be 13. Find the lower limit of the 90% confidence interval for the mean.

n = 49x̄ = 108σ = 1390%
lower limit =
3.Medium
n = 10, s = 8L = ?Ux̄ = 113.5E95%

A sample of 10 items has mean 113.5 and standard deviation s = 8. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 10x̄ = 113.5s = 895%t(9) = 2.262
lower limit =
4.Medium
n = 15, s = 17.5L = ?Ux̄ = 72E90%

A sample of 15 items has mean 72 and standard deviation s = 17.5. The population is roughly normal. Find the lower limit of the 90% confidence interval for the mean.

n = 15x̄ = 72s = 17.590%t(14) = 1.761
lower limit =
5.Hard
μ₁ − μ₂, t(29) = 2.0450LU = ?x̄₁ − x̄₂E95%

Two fertilisers are tested. Plot group 1: 8 plots, mean yield 60 kg, standard deviation 2.5 kg. Plot group 2: 23 plots, mean 52 kg, standard deviation 1.5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the upper limit of the 95% confidence interval for μ₁ − μ₂.

n₁ = 8x̄₁ = 60s₁ = 2.5n₂ = 23x̄₂ = 52s₂ = 1.595%t(29) = 2.045
upper limit = kg
6.Hard
σ = 22, n = ?x̄ − Ex̄ + Ex̄E = 2.599%

The population standard deviation is 22. How large a sample n do you need so that a 99% confidence interval for the mean has a margin of error of at most 2.5?

σ = 22E = 2.599%
n =

Answer key

  1. 1. E = 1.096
  2. 2. lower limit = 104.9
  3. 3. lower limit = 107.8
  4. 4. lower limit = 64.04
  5. 5. upper limit = 9.505 kg
  6. 6. n = 514

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