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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
n = 50, σ = 29LU = ?x̄ = 108E99%

A sample of 50 measurements has mean 108. The population standard deviation is known to be 29. Find the upper limit of the 99% confidence interval for the mean.

n = 50x̄ = 108σ = 2999%
upper limit =
2.Easy
108.35x̄118.6599%

A 99% confidence interval for a mean, computed from 64 observations with a known population standard deviation, is [108.35, 118.65]. What standard deviation σ was used?

[108.35, 118.65]n = 6499%
σ =
3.Medium
n = 10, s = 19LU = ?x̄ = 115.5E95%

A sample of 10 items has mean 115.5 and standard deviation s = 19. The population is roughly normal. Find the upper limit of the 95% confidence interval for the mean.

n = 10x̄ = 115.5s = 1995%t(9) = 2.262
upper limit =
4.Medium
n = 15, sd​ = 0.50LU = ?d̄ = 3.1E95%

The blood pressure of 15 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 3.1 and standard deviation 0.5. Find the upper limit of the 95% confidence interval for the mean difference.

n = 15d̄ = 3.1sd = 0.595%t(14) = 2.145
upper limit = mmHg
5.Hard
μ₁ − μ₂, t(19) = 2.8610LUx̄₁ − x̄₂E = ?99%

Two fertilisers are tested. Plot group 1: 7 plots, mean yield 31 kg, standard deviation 8 kg. Plot group 2: 14 plots, mean 23 kg, standard deviation 1 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 = 7x̄₁ = 31s₁ = 8n₂ = 14x̄₂ = 23s₂ = 199%t(19) = 2.861
E = kg
6.Hard
p ≈ 0.6, n = ?p̂ − Ep̂ + Ep̂E = 0.02590%

A pilot study suggests that about 0.6 of products are defective. 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 ≈ 0.6E = 0.02590%
n =

Answer key

  1. 1. upper limit = 118.6
  2. 2. σ = 15.99
  3. 3. upper limit = 129.1
  4. 4. upper limit = 3.377 mmHg
  5. 5. E = 6.054 kg
  6. 6. n = 1040

Full step-by-step solutions: practise this topic on examproblems.com.