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
LU = ?p̂ = 380/500E95%

In a poll of 500 randomly chosen voters, 380 support a proposal. Find the upper limit of the 95% confidence interval for the proportion of supporters.

n = 500x = 38095%
upper limit =
2.Easy
n = 49, σ = 16LU = ?x̄ = 29E95%

A sample of 49 measurements has mean 29. The population standard deviation is known to be 16. Find the upper limit of the 95% confidence interval for the mean.

n = 49x̄ = 29σ = 1695%
upper limit =
3.Medium
n = 10, s = 5.5L = ?Ux̄ = 55E90%

A sample of 10 items has mean 55 and standard deviation s = 5.5. The population is roughly normal. Find the lower limit of the 90% confidence interval for the mean.

n = 10x̄ = 55s = 5.590%t(9) = 1.833
lower limit =
4.Medium
n = 9, s = 6.5L = ?Ux̄ = 42E95%

A sample of 9 items has mean 42 and standard deviation s = 6.5. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 9x̄ = 42s = 6.595%t(8) = 2.306
lower limit =
5.Hard
μ₁ − μ₂, t(10) = 3.1690L = ?Ux̄₁ − x̄₂E99%

Two fertilisers are tested. Plot group 1: 6 plots, mean yield 26.5 kg, standard deviation 7 kg. Plot group 2: 6 plots, mean 31.5 kg, standard deviation 10 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the lower limit of the 99% confidence interval for μ₁ − μ₂.

n₁ = 6x̄₁ = 26.5s₁ = 7n₂ = 6x̄₂ = 31.5s₂ = 1099%t(10) = 3.169
lower limit = kg
6.Hard
σ = 25, n = ?x̄ − Ex̄ + Ex̄E = 399%

The population standard deviation is 25. How large a sample n do you need so that a 99% confidence interval for the mean has a margin of error of at most 3?

σ = 25E = 399%
n =

Answer key

  1. 1. upper limit = 0.7974
  2. 2. upper limit = 33.48
  3. 3. lower limit = 51.81
  4. 4. lower limit = 37
  5. 5. lower limit = −20.79 kg
  6. 6. n = 461

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