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
50.2x̄53.899%

A 99% confidence interval for a mean, computed from 100 observations with a known population standard deviation, is [50.2, 53.8]. What standard deviation σ was used?

[50.2, 53.8]n = 10099%
σ =
2.Easy
n = 49, σ = 5L = ?Ux̄ = 164.5E95%

A sample of 49 measurements has mean 164.5. The population standard deviation is known to be 5. Find the lower limit of the 95% confidence interval for the mean.

n = 49x̄ = 164.5σ = 595%
lower limit =
3.Medium
x̄E₁ = 4.399%, n = 36x̄E₂ = ?95%, n = 36

A 99% confidence interval for a mean, based on 36 observations and a known σ, has a margin of error of 4.3. What is the margin of error E₂ of a 95% interval from the same data?

99%n₁ = 36E₁ = 4.395%
E₂ =
4.Medium
n = 8, s = 1L = ?Ux̄ = 48.5E95%

A sample of 8 items has mean 48.5 and standard deviation s = 1. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 8x̄ = 48.5s = 195%t(7) = 2.365
lower limit =
5.Hard
n = 25Lσ = ?s = 495%

The diameters of 25 machined shafts have a sample standard deviation of 4 µm. Assuming the diameters are normally distributed, find the upper limit σ of the 95% confidence interval for the population standard deviation. With df = 24, 2.5% of the χ² distribution lies below 12.401 and 2.5% lies above 39.364.

n = 25s = 4 µmχ² = 12.401, 39.364
σ = µm
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. σ = 6.988
  2. 2. lower limit = 163.1
  3. 3. E₂ = 3.272
  4. 4. lower limit = 47.66
  5. 5. σ = 5.565 µm
  6. 6. n = 2401

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