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 50 times; the measurement standard deviation is known to be 21.5. How wide W is the 90% confidence interval for the true mean (upper limit minus lower limit)?

n = 50σ = 21.590%
W =
2.Easy
LUW = ?

A laboratory measures a quantity 16 times; the measurement standard deviation is known to be 18. How wide W is the 99% confidence interval for the true mean (upper limit minus lower limit)?

n = 16σ = 1899%
W =
3.Medium
x̄E₁ = 7.599%, n = 64x̄E₂ = ?99%, n = 16

A 99% confidence interval for a mean, based on 64 observations and a known σ, has a margin of error of 7.5. What is the margin of error E₂ if the same study uses 16 observations instead?

99%n₁ = 64E₁ = 7.5n₂ = 16
E₂ =
4.Medium
x̄E₁ = 5.190%, n = 25x̄E₂ = ?99%, n = 25

A 90% confidence interval for a mean, based on 25 observations and a known σ, has a margin of error of 5.1. What is the margin of error E₂ of a 99% interval from the same data?

90%n₁ = 25E₁ = 5.199%
E₂ =
5.Hard
n = 20Lσ = ?s = 395%

The diameters of 20 machined shafts have a sample standard deviation of 3 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 = 3 µmχ² = 8.907, 32.852
σ = µm
6.Hard
σ = 14, n = ?x̄ − Ex̄ + Ex̄E = 190%

The population standard deviation is 14. 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 1?

σ = 14E = 190%
n =

Answer key

  1. 1. W = 10
  2. 2. W = 23.18
  3. 3. E₂ = 15
  4. 4. E₂ = 7.986
  5. 5. σ = 4.382 µm
  6. 6. n = 531

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