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 = 49, σ = 14LUx̄ = 116E = ?99%

A sample of 49 measurements has mean 116. The population standard deviation is known to be 14. Find the margin of error E of a 99% confidence interval for the mean.

n = 49x̄ = 116σ = 1499%
E =
2.Easy
n = 64, σ = 10L = ?Ux̄ = 55.5E99%

A sample of 64 measurements has mean 55.5. The population standard deviation is known to be 10. Find the lower limit of the 99% confidence interval for the mean.

n = 64x̄ = 55.5σ = 1099%
lower limit =
3.Medium
x̄E₁ = 199%, 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 1. What is the margin of error E₂ of a 95% interval from the same data?

99%n₁ = 36E₁ = 195%
E₂ =
4.Medium
n = 12, s = 3LUx̄ = 117.5E = ?90%

A sample of 12 items has mean 117.5 and standard deviation s = 3. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 12x̄ = 117.5s = 390%t(11) = 1.796
E =
5.Hard
n = 20σ = ?Us = 8.495%

The diameters of 20 machined shafts have a sample standard deviation of 8.4 µm. Assuming the diameters are normally distributed, find the lower 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 = 8.4 µmχ² = 8.907, 32.852
σ = µm
6.Hard
μ₁ − μ₂, t(19) = 2.0930LUx̄₁ − x̄₂E = ?95%

Two fertilisers are tested. Plot group 1: 7 plots, mean yield 79 kg, standard deviation 8.5 kg. Plot group 2: 14 plots, mean 80.5 kg, standard deviation 3 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the margin of error E of the 95% confidence interval for μ₁ − μ₂.

n₁ = 7x̄₁ = 79s₁ = 8.5n₂ = 14x̄₂ = 80.5s₂ = 395%t(19) = 2.093
E = kg

Answer key

  1. 1. E = 5.152
  2. 2. lower limit = 52.28
  3. 3. E₂ = 0.7609
  4. 4. E = 1.555
  5. 5. σ = 6.388 µm
  6. 6. E = 5.215 kg

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