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 = 144, σ = 2LUx̄ = 53.5E = ?90%

A sample of 144 measurements has mean 53.5. The population standard deviation is known to be 2. Find the margin of error E of a 90% confidence interval for the mean.

n = 144x̄ = 53.5σ = 290%
E =
2.Easy
n = 50, σ = 4LU = ?x̄ = 184E95%

A sample of 50 measurements has mean 184. The population standard deviation is known to be 4. Find the upper limit of the 95% confidence interval for the mean.

n = 50x̄ = 184σ = 495%
upper limit =
3.Medium
n = 13, s = 6.5L = ?Ux̄ = 108E95%

A sample of 13 items has mean 108 and standard deviation s = 6.5. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 13x̄ = 108s = 6.595%t(12) = 2.179
lower limit =
4.Medium
n = 20, s = 18.5L = ?Ux̄ = 44.5E99%

A sample of 20 items has mean 44.5 and standard deviation s = 18.5. The population is roughly normal. Find the lower limit of the 99% confidence interval for the mean.

n = 20x̄ = 44.5s = 18.599%t(19) = 2.861
lower limit =
5.Hard
n = 20Lσ = ?s = 1295%

The diameters of 20 machined shafts have a sample standard deviation of 12 µm. Assuming the diameters are normally distributed, find the upper limit σ of the 95% confidence interval for the population standard deviation. With df = 19, 2.5% of the χ² distribution lies below 8.907 and 2.5% lies above 32.852.

n = 20s = 12 µmχ² = 8.907, 32.852
σ = µm
6.Hard
σ = 10, n = ?x̄ − Ex̄ + Ex̄E = 290%

The population standard deviation is 10. How large a sample n do you need so that a 90% confidence interval for the mean has a margin of error of at most 2?

σ = 10E = 290%
n =

Answer key

  1. 1. E = 0.2742
  2. 2. upper limit = 185.1
  3. 3. lower limit = 104.1
  4. 4. lower limit = 32.66
  5. 5. σ = 17.53 µm
  6. 6. n = 68

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