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
LUW = ?

A laboratory measures a quantity 16 times; the measurement standard deviation is known to be 4. How wide W is the 90% confidence interval for the true mean (upper limit minus lower limit)?

n = 16σ = 490%
W =
2.Easy
LU = ?p̂ = 260/1000E90%

In a poll of 1000 randomly chosen voters, 260 support a proposal. Find the upper limit of the 90% confidence interval for the proportion of supporters.

n = 1000x = 26090%
upper limit =
3.Medium
x̄E₁ = 790%, n = 25x̄E₂ = ?95%, n = 25

A 90% confidence interval for a mean, based on 25 observations and a known σ, has a margin of error of 7. What is the margin of error E₂ of a 95% interval from the same data?

90%n₁ = 25E₁ = 795%
E₂ =
4.Medium
n = 20, s = 20LUx̄ = 45.5E = ?90%

A sample of 20 items has mean 45.5 and standard deviation s = 20. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 20x̄ = 45.5s = 2090%t(19) = 1.729
E =
5.Hard
σ = 36, n = ?x̄ − Ex̄ + Ex̄E = 0.590%

The population standard deviation is 36. 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 0.5?

σ = 36E = 0.590%
n =
6.Hard
μ₁ − μ₂, t(14) = 1.7610LUx̄₁ − x̄₂E = ?90%

Two fertilisers are tested. Plot group 1: 8 plots, mean yield 17.5 kg, standard deviation 3 kg. Plot group 2: 8 plots, mean 21.5 kg, standard deviation 8 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the margin of error E of the 90% confidence interval for μ₁ − μ₂.

n₁ = 8x̄₁ = 17.5s₁ = 3n₂ = 8x̄₂ = 21.5s₂ = 890%t(14) = 1.761
E = kg

Answer key

  1. 1. W = 3.29
  2. 2. upper limit = 0.2828
  3. 3. E₂ = 8.34
  4. 4. E = 7.732
  5. 5. n = 14029
  6. 6. E = 5.32 kg

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