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 = 100, σ = 8LU = ?x̄ = 30.5E99%

A sample of 100 measurements has mean 30.5. The population standard deviation is known to be 8. Find the upper limit of the 99% confidence interval for the mean.

n = 100x̄ = 30.5σ = 899%
upper limit =
2.Easy
n = 64, σ = 13LUx̄ = 104E = ?95%

A sample of 64 measurements has mean 104. The population standard deviation is known to be 13. Find the margin of error E of a 95% confidence interval for the mean.

n = 64x̄ = 104σ = 1395%
E =
3.Medium
n = 9, s = 5.5LU = ?x̄ = 55E99%

A sample of 9 items has mean 55 and standard deviation s = 5.5. The population is roughly normal. Find the upper limit of the 99% confidence interval for the mean.

n = 9x̄ = 55s = 5.599%t(8) = 3.355
upper limit =
4.Medium
μ₁ − μ₂0LUx̄₁ − x̄₂E = ?99%

The battery life of two phone models is compared. Model 1: 60 phones, mean 60.5 h, known standard deviation 12 h. Model 2: 60 phones, mean 67 h, known standard deviation 13 h. Find the margin of error E of the 99% confidence interval for μ₁ − μ₂.

n₁ = 60x̄₁ = 60.5 hσ₁ = 12 hn₂ = 60x̄₂ = 67 hσ₂ = 13 h99%
E = h
5.Hard
p = 0.5, n = ?p̂ − Ep̂ + Ep̂E = 0.02595%

Nothing is known in advance about the proportion of defective products. How many products n must be inspected so that a 95% confidence interval for the proportion has a margin of error of at most 0.025?

p = 0.5E = 0.02595%
n =
6.Hard
σ = 18, n = ?x̄ − Ex̄ + Ex̄E = 0.599%

The population standard deviation is 18. 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 0.5?

σ = 18E = 0.599%
n =

Answer key

  1. 1. upper limit = 32.56
  2. 2. E = 3.185
  3. 3. upper limit = 61.15
  4. 4. E = 5.884 h
  5. 5. n = 1537
  6. 6. n = 8600

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