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
L = ?Up̂ = 284/400E95%

In a poll of 400 randomly chosen voters, 284 support a proposal. Find the lower limit of the 95% confidence interval for the proportion of supporters.

n = 400x = 28495%
lower limit =
2.Easy
113.57x̄116.4399%

A 99% confidence interval for a mean, computed from 81 observations with a known population standard deviation, is [113.57, 116.43]. What standard deviation σ was used?

[113.57, 116.43]n = 8199%
σ =
3.Medium
x̄E₁ = 9.690%, n = 64x̄E₂ = ?90%, n = 576

A 90% confidence interval for a mean, based on 64 observations and a known σ, has a margin of error of 9.6. What is the margin of error E₂ if the same study uses 576 observations instead?

90%n₁ = 64E₁ = 9.6n₂ = 576
E₂ =
4.Medium
n = 7, s = 16LU = ?x̄ = 14E95%

A sample of 7 items has mean 14 and standard deviation s = 16. The population is roughly normal. Find the upper limit of the 95% confidence interval for the mean.

n = 7x̄ = 14s = 1695%t(6) = 2.447
upper limit =
5.Hard
σ = 4, n = ?x̄ − Ex̄ + Ex̄E = 190%

The population standard deviation is 4. 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 = 4E = 190%
n =
6.Hard
μ₁ − μ₂, t(15) = 2.9470L = ?Ux̄₁ − x̄₂E99%

Two fertilisers are tested. Plot group 1: 10 plots, mean yield 79.5 kg, standard deviation 2 kg. Plot group 2: 7 plots, mean 84 kg, standard deviation 2.5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the lower limit of the 99% confidence interval for μ₁ − μ₂.

n₁ = 10x̄₁ = 79.5s₁ = 2n₂ = 7x̄₂ = 84s₂ = 2.599%t(15) = 2.947
lower limit = kg

Answer key

  1. 1. lower limit = 0.6655
  2. 2. σ = 4.996
  3. 3. E₂ = 3.2
  4. 4. upper limit = 28.8
  5. 5. n = 44
  6. 6. lower limit = −7.715 kg

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