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 = 408/800E90%

In a poll of 800 randomly chosen voters, 408 support a proposal. Find the lower limit of the 90% confidence interval for the proportion of supporters.

n = 800x = 40890%
lower limit =
2.Easy
L = ?Up̂ = 270/1000E95%

In a poll of 1000 randomly chosen voters, 270 support a proposal. Find the lower limit of the 95% confidence interval for the proportion of supporters.

n = 1000x = 27095%
lower limit =
3.Medium
x̄E₁ = 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 3. What is the margin of error E₂ of a 95% interval from the same data?

99%n₁ = 36E₁ = 395%
E₂ =
4.Medium
n = 21, s = 5LUx̄ = 118E = ?90%

A sample of 21 items has mean 118 and standard deviation s = 5. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 21x̄ = 118s = 590%t(20) = 1.725
E =
5.Hard
μ₁ − μ₂, t(20) = 2.8450LUx̄₁ − x̄₂E = ?99%

Two fertilisers are tested. Plot group 1: 10 plots, mean yield 72.5 kg, standard deviation 1 kg. Plot group 2: 12 plots, mean 79 kg, standard deviation 2 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the margin of error E of the 99% confidence interval for μ₁ − μ₂.

n₁ = 10x̄₁ = 72.5s₁ = 1n₂ = 12x̄₂ = 79s₂ = 299%t(20) = 2.845
E = kg
6.Hard
p = 0.5, n = ?p̂ − Ep̂ + Ep̂E = 0.02590%

Nothing is known in advance about the proportion of defective products. How many products n must be inspected so that a 90% confidence interval for the proportion has a margin of error of at most 0.025?

p = 0.5E = 0.02590%
n =

Answer key

  1. 1. lower limit = 0.4809
  2. 2. lower limit = 0.2425
  3. 3. E₂ = 2.283
  4. 4. E = 1.882
  5. 5. E = 1.983 kg
  6. 6. n = 1083

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