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
LUW = ?

A laboratory measures a quantity 30 times; the measurement standard deviation is known to be 20.5. How wide W is the 99% confidence interval for the true mean (upper limit minus lower limit)?

n = 30σ = 20.599%
W =
2.Easy
n = 49, σ = 10LU = ?x̄ = 113.5E95%

A sample of 49 measurements has mean 113.5. The population standard deviation is known to be 10. Find the upper limit of the 95% confidence interval for the mean.

n = 49x̄ = 113.5σ = 1095%
upper limit =
3.Medium
n = 21, s = 3.5LU = ?x̄ = 23.5E95%

A sample of 21 items has mean 23.5 and standard deviation s = 3.5. The population is roughly normal. Find the upper limit of the 95% confidence interval for the mean.

n = 21x̄ = 23.5s = 3.595%t(20) = 2.086
upper limit =
4.Medium
x̄E₁ = 6.999%, n = 36x̄E₂ = ?99%, n = 324

A 99% confidence interval for a mean, based on 36 observations and a known σ, has a margin of error of 6.9. What is the margin of error E₂ if the same study uses 324 observations instead?

99%n₁ = 36E₁ = 6.9n₂ = 324
E₂ =
5.Hard
σ = 18, n = ?x̄ − Ex̄ + Ex̄E = 595%

The population standard deviation is 18. 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 5?

σ = 18E = 595%
n =
6.Hard
μ₁ − μ₂, t(15) = 1.7530LUx̄₁ − x̄₂E = ?90%

Two fertilisers are tested. Plot group 1: 11 plots, mean yield 84.5 kg, standard deviation 1 kg. Plot group 2: 6 plots, mean 73 kg, standard deviation 6 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 = 11x̄₁ = 84.5s₁ = 1n₂ = 6x̄₂ = 73s₂ = 690%t(15) = 1.753
E = kg

Answer key

  1. 1. W = 19.28
  2. 2. upper limit = 116.3
  3. 3. upper limit = 25.09
  4. 4. E₂ = 2.3
  5. 5. n = 50
  6. 6. E = 3.166 kg

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