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 = 64, σ = 26LU = ?x̄ = 180E95%

A sample of 64 measurements has mean 180. The population standard deviation is known to be 26. Find the upper limit of the 95% confidence interval for the mean.

n = 64x̄ = 180σ = 2695%
upper limit =
2.Easy
n = 80, σ = 29L = ?Ux̄ = 93E95%

A sample of 80 measurements has mean 93. The population standard deviation is known to be 29. Find the lower limit of the 95% confidence interval for the mean.

n = 80x̄ = 93σ = 2995%
lower limit =
3.Medium
x̄E₁ = 299%, n = 25x̄E₂ = ?90%, n = 25

A 99% confidence interval for a mean, based on 25 observations and a known σ, has a margin of error of 2. What is the margin of error E₂ of a 90% interval from the same data?

99%n₁ = 25E₁ = 290%
E₂ =
4.Medium
x̄E₁ = 7.699%, n = 64x̄E₂ = ?90%, n = 64

A 99% confidence interval for a mean, based on 64 observations and a known σ, has a margin of error of 7.6. What is the margin of error E₂ of a 90% interval from the same data?

99%n₁ = 64E₁ = 7.690%
E₂ =
5.Hard
μ₁ − μ₂, t(12) = 2.1790L = ?Ux̄₁ − x̄₂E95%

Two fertilisers are tested. Plot group 1: 9 plots, mean yield 42 kg, standard deviation 10 kg. Plot group 2: 5 plots, mean 43.5 kg, standard deviation 1.5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the lower limit of the 95% confidence interval for μ₁ − μ₂.

n₁ = 9x̄₁ = 42s₁ = 10n₂ = 5x̄₂ = 43.5s₂ = 1.595%t(12) = 2.179
lower limit = kg
6.Hard
σ = 33, n = ?x̄ − Ex̄ + Ex̄E = 0.595%

The population standard deviation is 33. 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 0.5?

σ = 33E = 0.595%
n =

Answer key

  1. 1. upper limit = 186.4
  2. 2. lower limit = 86.65
  3. 3. E₂ = 1.277
  4. 4. E₂ = 4.853
  5. 5. lower limit = −11.48 kg
  6. 6. n = 16735

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