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 = 200, σ = 8L = ?Ux̄ = 71E95%

A sample of 200 measurements has mean 71. The population standard deviation is known to be 8. Find the lower limit of the 95% confidence interval for the mean.

n = 200x̄ = 71σ = 895%
lower limit =
2.Easy
LUW = ?

A laboratory measures a quantity 30 times; the measurement standard deviation is known to be 5.5. How wide W is the 95% confidence interval for the true mean (upper limit minus lower limit)?

n = 30σ = 5.595%
W =
3.Medium
n = 30, s = 18.5LUx̄ = 28.5E = ?95%

A sample of 30 items has mean 28.5 and standard deviation s = 18.5. The population is roughly normal. Find the margin of error E of a 95% confidence interval for the mean.

n = 30x̄ = 28.5s = 18.595%t(29) = 2.045
E =
4.Medium
n = 8, s = 13LUx̄ = 85E = ?90%

A sample of 8 items has mean 85 and standard deviation s = 13. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 8x̄ = 85s = 1390%t(7) = 1.895
E =
5.Hard
σ = 36, n = ?x̄ − Ex̄ + Ex̄E = 199%

The population standard deviation is 36. 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 1?

σ = 36E = 199%
n =
6.Hard
p = 0.5, n = ?p̂ − Ep̂ + Ep̂E = 0.0295%

Nothing is known in advance about the proportion of defective products. How many products n must be inspected so that a 95% confidence interval for the proportion has a margin of error of at most 0.02?

p = 0.5E = 0.0295%
n =

Answer key

  1. 1. lower limit = 69.89
  2. 2. W = 3.936
  3. 3. E = 6.907
  4. 4. E = 8.71
  5. 5. n = 8600
  6. 6. n = 2401

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