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 = 215/250E95%

In a poll of 250 randomly chosen voters, 215 support a proposal. Find the upper limit of the 95% confidence interval for the proportion of supporters.

n = 250x = 21595%
upper limit =
2.Easy
n = 64, σ = 19L = ?Ux̄ = 189E90%

A sample of 64 measurements has mean 189. The population standard deviation is known to be 19. Find the lower limit of the 90% confidence interval for the mean.

n = 64x̄ = 189σ = 1990%
lower limit =
3.Medium
n = 16, sd​ = 6.20LUd̄ = 5.8E = ?90%

The blood pressure of 16 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 5.8 and standard deviation 6.2. Find the margin of error E of the 90% confidence interval for the mean difference.

n = 16d̄ = 5.8sd = 6.290%t(15) = 1.753
E = mmHg
4.Medium
n = 16, s = 9.5LUx̄ = 58.5E = ?99%

A sample of 16 items has mean 58.5 and standard deviation s = 9.5. The population is roughly normal. Find the margin of error E of a 99% confidence interval for the mean.

n = 16x̄ = 58.5s = 9.599%t(15) = 2.947
E =
5.Hard
μ₁ − μ₂, t(20) = 1.7250LU = ?x̄₁ − x̄₂E90%

Two fertilisers are tested. Plot group 1: 8 plots, mean yield 38 kg, standard deviation 6 kg. Plot group 2: 14 plots, mean 31.5 kg, standard deviation 9 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the upper limit of the 90% confidence interval for μ₁ − μ₂.

n₁ = 8x̄₁ = 38s₁ = 6n₂ = 14x̄₂ = 31.5s₂ = 990%t(20) = 1.725
upper limit = kg
6.Hard
μ₁ − μ₂, t(24) = 2.0640L = ?Ux̄₁ − x̄₂E95%

Two fertilisers are tested. Plot group 1: 12 plots, mean yield 83 kg, standard deviation 6 kg. Plot group 2: 14 plots, mean 71 kg, standard deviation 5 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the lower limit of the 95% confidence interval for μ₁ − μ₂.

n₁ = 12x̄₁ = 83s₁ = 6n₂ = 14x̄₂ = 71s₂ = 595%t(24) = 2.064
lower limit = kg

Answer key

  1. 1. upper limit = 0.903
  2. 2. lower limit = 185.1
  3. 3. E = 2.717 mmHg
  4. 4. E = 6.999
  5. 5. upper limit = 12.68 kg
  6. 6. lower limit = 7.55 kg

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